Wow.
It really is amazing that the year is over. It seems like it has gone by so fast...it's like I remember people in class asking how to take a derivative, and I feel like it was days ago...wait, that was days ago, like Monday when we reviewed. :-P.
Jokes aside, I can't express how awesome this year has been for me in Calculus. It feels like we flew right through it, and it was not as bad as some people made it out to be. Calculus is pretty easy once you get the concepts down (derivatives and integrals). It is of course taught by an amazing teacher, so I know that everyone after me will do just fine with very little effort.
I first want to congratulate and acknowledge Mrs. Brandi Robinson for being an amazing teacher. Not only did you have a baby and manage to keep your math classes running, but you also taught us so many things and prepared us so well for the AP exam. I can honestly say that I took the AP exam with absolutely no studying outside of the school day, and I'm positive I did well on it. I would not be able to say that without you, and I greatly thank you and appreciate everything you've done for me and the class especially.
Second, I want to say that I could not have done so well in Calculus without all of my classmates as well. The reason I was able to take the AP without studying is because of you guys, mainly. You guys pestered me and annoyed me and asked as many questions as you could possibly come up with, sometimes asking the same exact question without realizing it, and I thank you all for it. Through all of the explaining and answering of your questions, I was able to study almost every class period of my day. You guys have made my year successful, and I want to thank you for that. I also hope that I have helped make your year just as successful, because that would only be the fair thing :-).
Last, I want to thank Chelsea specifically. Of every classmate in Calculus, she has been the most useful to me. Whether it was her asking a million and one questions or whether it was discussing calculus problems over AIM, she helped me in a million ways, and I owe my deepest gratitude and thanks to her for all of her help. :-)
Overall, Calculus AB has been a complete success on so many levels. Not only will it get me credit hours in college, but it really has furthered my knowledge in mathematics and Calculus specifically, which is going to help my career (Engineering) in so many ways.
P.S. I just want to thank you again, B-Rob, for being an amazing teacher and mentor. I cannot fathom the words to describe how awesome you have been to me this year with all of your help and support. With that being said, I hope you understand how much I truly cherish the teachings and knowledge you have passed to me.
-John
Sunday, May 9, 2010
final post
alright, well some of the things i've gotten comfortable doing this year in calculus is the first and second derivative test. since those were basically the first things we did this year, i learned those the best, and i got kinda lazy throughout the rest of the year, so that's why i was the best at that.
For this post i am going to go into detail on the second derivative test to find all possible points of inflection and intervals of concavity. remember, points of inflection only happen where there is a change of concavity.
Example: f'(x)= 6/(x^(2)+3)
First, you have to take the derivative of that, and you have to use the quotient rule, so the beginning of the problem will look like, [(x^(2)+3)(0)-6(2x)]/(x^(2)+3)^(2), which simplifies to -12x/(x^(2)+3)^2 remember, that was just the first derivative.
Second step is to take the derivative of the first derivative, that would make this step called taking the second derivative.
Once again u need to use the quotient rule, so f''(x)={(x2+3)^2-(12)-[(-12x)2(x^(2)+3)2x} all that over (x^(2)+3)^4 then you get a bunch of stuff, then you simplify, then you cancel, so I am just going to type the end answer of the second derivative. Which is, (3)(6)(x+1)(x-1) all over (x^2+3)^3
The possible points of inflection are found in the numerator of the finished second derivative, in this case, if you look, it would be x=1, and x=-1
so then you set up your points, (-infinity, -1) u (-1, 1) u (1, infinity)
then you plug in. f''(-2)= positive value f''(0)=negative value f''(2)=positive value
then you know that your intervals concave up at (-infinity, -1) u (1,infinity) or x<1,>1
and it is concave down at (-1,1) or -1
and you're points of inflection are x=-1, and x=1
okay, one thing i wish i would have done was do my homework at the beginning of the year, because that would have made learning all the other stuff throughout the year much easier. and my advice to anyone else taking this class is to learn derivatives, integrals, related rates, substitution, limits, and implicit derivatives really well, because that's pretty much all the main focal points of the ap test and calculus in general. and thanks ms robinson for teaching me so much and being such a cool teacher :)
For this post i am going to go into detail on the second derivative test to find all possible points of inflection and intervals of concavity. remember, points of inflection only happen where there is a change of concavity.
Example: f'(x)= 6/(x^(2)+3)
First, you have to take the derivative of that, and you have to use the quotient rule, so the beginning of the problem will look like, [(x^(2)+3)(0)-6(2x)]/(x^(2)+3)^(2), which simplifies to -12x/(x^(2)+3)^2 remember, that was just the first derivative.
Second step is to take the derivative of the first derivative, that would make this step called taking the second derivative.
Once again u need to use the quotient rule, so f''(x)={(x2+3)^2-(12)-[(-12x)2(x^(2)+3)2x} all that over (x^(2)+3)^4 then you get a bunch of stuff, then you simplify, then you cancel, so I am just going to type the end answer of the second derivative. Which is, (3)(6)(x+1)(x-1) all over (x^2+3)^3
The possible points of inflection are found in the numerator of the finished second derivative, in this case, if you look, it would be x=1, and x=-1
so then you set up your points, (-infinity, -1) u (-1, 1) u (1, infinity)
then you plug in. f''(-2)= positive value f''(0)=negative value f''(2)=positive value
then you know that your intervals concave up at (-infinity, -1) u (1,infinity) or x<1,>1
and it is concave down at (-1,1) or -1
and you're points of inflection are x=-1, and x=1
okay, one thing i wish i would have done was do my homework at the beginning of the year, because that would have made learning all the other stuff throughout the year much easier. and my advice to anyone else taking this class is to learn derivatives, integrals, related rates, substitution, limits, and implicit derivatives really well, because that's pretty much all the main focal points of the ap test and calculus in general. and thanks ms robinson for teaching me so much and being such a cool teacher :)
Ricky's Last Blog
After all the anticipation, its finally over. High school and more importantly CALCULUS. I'm not a math person as many of u know but im glad i have been in advanced math and in calculus with all of you. i love each and every one of you and im glad to call yall my classmates. From watching ryan get yelled at to making stupid math jokes. yall are amazing. i would be lost without most of you so i would like to say thanks for putting up with me sometimes.
I will have many things that stick with me from calculus but lets see what i can really remember. first and second derivative tests is something i def cant forget. WE DID IT A MILLION TIMES.
I will def remember limit rules.
1. If the degree of the top is larger than the degree of the bottom, the limit approaches infinity
2. If the degree of the bottom is larger than the degree of the tip, the limit approaches zero
3. If the degree of the bottom is equal to the degree of the top, then you make a fraction out of the coefficients in front of the largest degree.
I know the optimization steps i just suck at doing them hahaahahah i know how to take integrals and how to substitute. i know eintegration and many other useful tools that i have learned along the way of my calculus year.
One thing i have learned more than anything is to never give up and strive for something better. i didnt ahve to take calculus as a senior buti chose to and im glad i did. the hard work will help me in college just like it will help the rest of the class.
To Brandi:
Even though i wanted to kill myself during the year im glad to have had you as a teacher these past two years. From making you laugh to me almost crying cuz your tests were beast i had a great time. This year was a great one w/ alot of things that will help me in the future. thank you for being there for me and being my teacher even though im not the easiest to teach.
TO THE JUNIORS:
I LOVE YALL JUST AS IF YALL WERE SENIORS. I WISH YALLL COULD GRADUATE WITH US BUT YALL HAVE YALLS OWN THING TO DO NEXT YEAR. IMA BE AROUND NEXT YEAR BTW SO YALL CANT MISS ME TOOO MUCH :D
TO THE CLASS OF 2010:
LETS DO THIS :) WE WORKED OUR A$$E$ OFF AND ITS GONNA PAY OFF. I LOVE YOU ALL AS IF YOU WERE MY BROTHERS AND SISTERS. IN FACT YALL ARE LIKE BROTHERS AND SISTERS. IF ANY OFYOU NEED ANYTHING IN THE FUTURE U KNOW THE NUMBER.
Signing out,
Ricky Johnson ;)
I will have many things that stick with me from calculus but lets see what i can really remember. first and second derivative tests is something i def cant forget. WE DID IT A MILLION TIMES.
I will def remember limit rules.
1. If the degree of the top is larger than the degree of the bottom, the limit approaches infinity
2. If the degree of the bottom is larger than the degree of the tip, the limit approaches zero
3. If the degree of the bottom is equal to the degree of the top, then you make a fraction out of the coefficients in front of the largest degree.
I know the optimization steps i just suck at doing them hahaahahah i know how to take integrals and how to substitute. i know eintegration and many other useful tools that i have learned along the way of my calculus year.
One thing i have learned more than anything is to never give up and strive for something better. i didnt ahve to take calculus as a senior buti chose to and im glad i did. the hard work will help me in college just like it will help the rest of the class.
To Brandi:
Even though i wanted to kill myself during the year im glad to have had you as a teacher these past two years. From making you laugh to me almost crying cuz your tests were beast i had a great time. This year was a great one w/ alot of things that will help me in the future. thank you for being there for me and being my teacher even though im not the easiest to teach.
TO THE JUNIORS:
I LOVE YALL JUST AS IF YALL WERE SENIORS. I WISH YALLL COULD GRADUATE WITH US BUT YALL HAVE YALLS OWN THING TO DO NEXT YEAR. IMA BE AROUND NEXT YEAR BTW SO YALL CANT MISS ME TOOO MUCH :D
TO THE CLASS OF 2010:
LETS DO THIS :) WE WORKED OUR A$$E$ OFF AND ITS GONNA PAY OFF. I LOVE YOU ALL AS IF YOU WERE MY BROTHERS AND SISTERS. IN FACT YALL ARE LIKE BROTHERS AND SISTERS. IF ANY OFYOU NEED ANYTHING IN THE FUTURE U KNOW THE NUMBER.
Signing out,
Ricky Johnson ;)
Final Reflection
Well, the class we all anticipated to fail is finally over and I think most of us learned a lot of calculus this year.
Some topics I caught on to right away such as tangent line and normal line since it was only taking a derivative and plugging in numbers. I also learned RRAM, LRAM, TRAM, and MRAM right away. This is partly because I did both my comments on these topics weekly for almost 2 months. It really is just plugging in formulas.
Other topics such as optimization and integration took longer to catch on too. I did not understand optimization at all until Brob gave us steps on the board one day. Those steps applied to every problem we saw. I think its easier to follow steps then to have to decipher the problem by yourself, at leas it is for me. Integration is not a hard topic, but it just took time to catch on too. A LOT of practice problems were done especially substitution problems. I still forget my +c sometimes though. I never really did get into the habit of putting it. I also did not know how to do anything in my calculator until around the last month of school. That is when John started giving me funny looks when correcting APs because I tried to do everything by hand. Who knew those a hundred something dollars would actually be worth it.
And finally, the topics that I still struggle with are graphs, angle of elevation, and related rates. Graphs I never did get from day one. I did get a little better with them since they were on EVERY AP, but I would have liked to have had a better understanding on them. I always struggled with word problems hence my problem with angle of elevation and related rates. Every problem differs so these cannot have a set of rules like optimization does. I have a problem with drawing the picture correctly and picking out the given and what we are looking for.
All in all, I feel it was a pretty successful year, and I want to thank you brob for HOPEFULLY getting me out of calculus in college; although, I cannot picture next year without it.
Also, a thanks to all my classmates for asking plenty of questions, so I did not have too =)
And a thanks to John for answering my thousands of questions even though many of them were repeated.
I will miss all of you!
Some topics I caught on to right away such as tangent line and normal line since it was only taking a derivative and plugging in numbers. I also learned RRAM, LRAM, TRAM, and MRAM right away. This is partly because I did both my comments on these topics weekly for almost 2 months. It really is just plugging in formulas.
Other topics such as optimization and integration took longer to catch on too. I did not understand optimization at all until Brob gave us steps on the board one day. Those steps applied to every problem we saw. I think its easier to follow steps then to have to decipher the problem by yourself, at leas it is for me. Integration is not a hard topic, but it just took time to catch on too. A LOT of practice problems were done especially substitution problems. I still forget my +c sometimes though. I never really did get into the habit of putting it. I also did not know how to do anything in my calculator until around the last month of school. That is when John started giving me funny looks when correcting APs because I tried to do everything by hand. Who knew those a hundred something dollars would actually be worth it.
And finally, the topics that I still struggle with are graphs, angle of elevation, and related rates. Graphs I never did get from day one. I did get a little better with them since they were on EVERY AP, but I would have liked to have had a better understanding on them. I always struggled with word problems hence my problem with angle of elevation and related rates. Every problem differs so these cannot have a set of rules like optimization does. I have a problem with drawing the picture correctly and picking out the given and what we are looking for.
All in all, I feel it was a pretty successful year, and I want to thank you brob for HOPEFULLY getting me out of calculus in college; although, I cannot picture next year without it.
Also, a thanks to all my classmates for asking plenty of questions, so I did not have too =)
And a thanks to John for answering my thousands of questions even though many of them were repeated.
I will miss all of you!
sarah's final blog part 2.
OMG I ALMOST FORGOT!
To B-ROB: you are an AMAZING teacher. I don't care what anyone says, hands-down.. best teacher at riverside academy. you have so much dedication for your students and you believe in all of us. even the annoying ones in the class... ;) you are one of the only teachers i know that will work with you in all of your extra hours UNTIL you get it. no matter how long it takes, you will make it click in our brains. which you did for most of us. i wish i could put a note on here for all incoming calc students saying that brob is willing to help as long as you're willing to put forth the effort. that is one thing that i've learned also, which i'm very glad i did. i can honestly say i think i'm speaking on behalf of the entire class when i say: WE LOVE YOU BROB. thank you for believing in us.
To B-ROB: you are an AMAZING teacher. I don't care what anyone says, hands-down.. best teacher at riverside academy. you have so much dedication for your students and you believe in all of us. even the annoying ones in the class... ;) you are one of the only teachers i know that will work with you in all of your extra hours UNTIL you get it. no matter how long it takes, you will make it click in our brains. which you did for most of us. i wish i could put a note on here for all incoming calc students saying that brob is willing to help as long as you're willing to put forth the effort. that is one thing that i've learned also, which i'm very glad i did. i can honestly say i think i'm speaking on behalf of the entire class when i say: WE LOVE YOU BROB. thank you for believing in us.
Kaitlyn's Final Reflection
Well after anticipating all year, it's finally here. My last few days of high school. First I just want to say how bittersweet this class was for me. The class itself, i loved it! The people, the messing around, the stressing out, the late night mini van trips, it was unforgettable. I really enjoyed getting to know everyone and love our ability to have fun yet still get a lot of work done. Now for the bitter part...the actually calculus. I'm pretty sure it's safe to say i suck at it. But hey, it's not the end of the world. Don't worry, i don't plan on building bridges or roller coasters in my future, so y'all should be safe ;)
Now onto the "concept" that never gave up on me and kept running into my skull until it finally got into my brain...
what else could it be..... AVERAGE VALUE!
It's just such a simple integral problem, how can anyone get this wrong. The formula is 1/b-a bSa f(x). You simply just plug in to the formula with what you were given. And half the time it's in the calculator portion so you just have to plug the integral in your calculator then times it by 1/b-a. Voila, you get a beautiful answer that you actually think is right :) AMEN to that.
Just so i don't seem like i only accomplished one thing in calculus all year, some other things i understood were average rate of change, mean value theorem, simple derivatives and integrals, HORIZONTAL TANGENTS, and i'm sure there are a couple of others.
So onto my farewells:
my seniors- We've had an amazing run. We're all so close and we worked hard to get where we are. No matter how mean i may come off sometimes, I love each and every one of y'all and wish every one luck in their future endeavors. Now let's finish this year off right and make a name.
oh let's doooo it
the juniors- i absolutely love y'all. i never really talked to y'all much before this class but i'm so glad that we had it together. Every one of y'all cracks me up, and i know y'all will be successful b/c of how determined you are. Keep it up and don't slack off, and have fun in calculs bc next year. I might miss you guys ;)
B-robbbb- thanks for putting up with me these last two years. You believed in me and kept pushing me even when i said it was impossible to stick this what i call "garbage" in my brain. I know i didn't catch on to a lot at first, but i did try and i truly believe no other teacher could put up with us as well as you did. You're an awesome person and i truly admire you and all of your accomplishments. Thanks again for everything :)
Now i think it's time to close this blog, my LAST one.
Goodbye Calculus, Goodbye Riverside, Hello Life :)
Now onto the "concept" that never gave up on me and kept running into my skull until it finally got into my brain...
what else could it be..... AVERAGE VALUE!
It's just such a simple integral problem, how can anyone get this wrong. The formula is 1/b-a bSa f(x). You simply just plug in to the formula with what you were given. And half the time it's in the calculator portion so you just have to plug the integral in your calculator then times it by 1/b-a. Voila, you get a beautiful answer that you actually think is right :) AMEN to that.
Just so i don't seem like i only accomplished one thing in calculus all year, some other things i understood were average rate of change, mean value theorem, simple derivatives and integrals, HORIZONTAL TANGENTS, and i'm sure there are a couple of others.
So onto my farewells:
my seniors- We've had an amazing run. We're all so close and we worked hard to get where we are. No matter how mean i may come off sometimes, I love each and every one of y'all and wish every one luck in their future endeavors. Now let's finish this year off right and make a name.
oh let's doooo it
the juniors- i absolutely love y'all. i never really talked to y'all much before this class but i'm so glad that we had it together. Every one of y'all cracks me up, and i know y'all will be successful b/c of how determined you are. Keep it up and don't slack off, and have fun in calculs bc next year. I might miss you guys ;)
B-robbbb- thanks for putting up with me these last two years. You believed in me and kept pushing me even when i said it was impossible to stick this what i call "garbage" in my brain. I know i didn't catch on to a lot at first, but i did try and i truly believe no other teacher could put up with us as well as you did. You're an awesome person and i truly admire you and all of your accomplishments. Thanks again for everything :)
Now i think it's time to close this blog, my LAST one.
Goodbye Calculus, Goodbye Riverside, Hello Life :)
sarah's final blog.
wow. I can't believe it's finally over. In a few days, i'll no longer by an underclassmen. I never realized how hard this was gonna be until it actually happened. I sound like i'm leaving the earth or something. ha, sorry. This is only my junior year and I'm already freaking out. I'm a big baby.
To my seniors: I love you guys more than you know. Every last one of you. Including Mher, although he always seems to not be in class. Yall had an awesome year, I can tell. I hope my senior years proves to be just as great. You guys will be missed, EXTREMELY. especially those of you who have been at RA since I first walked in the front door when I was 4. I always looked up to you guys... cuz yall were older :) and it's so weird to think that next year, we will be the role models. It still hasn't hit me yet.
To my juniors: Well, what can I say. it's been one heck of a ride.. From preschool, to middle school, to soon-to-be seniors. The five of you in the calc class are the people I am most close to out of the ENTIRE jr class. because I spend 90% of my day with you mon-fri... on weekends @ math trips, and during the summer @ practices. I love yall more than you can imagine. I can't wait for next year's calc BC class, it will be fun with just the six of us :)
So i'll stop being all mushy for a moment and talk about calc this year.
Most helpful thing: working in groups at the end of year to go over what you missed on the practice ap tests. one-on-one with another student that will actually make you do your work (thanks ellie) helped me more than you can understand. best idea yet B-ROB.
Thing i struggled with most: integration. i honestly still am not 100% with it, idk what it is. substitution, ln, tan inverse. none of it came to me easily. more practice was needed probably? idk.
Thing I picked up on the quickest: the derivative formulas. I can still say them to you probably quicker than anyone in the class. all those derivative practice sheets in the beginning were SOOOO helpful.
My epiphany of the year: the riemann sum formulas!!!!!!!!! honestly, i didn't understand all that f(a) + f(2 + a) stuff. and multiply by delta x whatever. it must easier when taught that TRAM is
b' + b'' / 2 (n) + b'' + b''' /2 (n). also the LRAM and RRAM are easier when taught that you add to x's divide by n (start all the way to left with LRAM and 2nd number with RRAM). that literally clicked in my head 2 days before the exam.
so, even though I don't want it to, this year is coming to a close. and quick too. I'm going to miss all you entirely too much. I will probably cry... a lot. just because I'm about to be a senior. i'll be sad everyday in calculus when i realize how small the class is. (& when i realize that mher IS actually not there). we had a great year, from partying it up with mr. st pierre to re-partying it up with brob. & of course getting people to sneak out of school to buy us some soft drinks because ricky never brings his stuff! i will miss it all.
GOOD LUCK TO YOU, seniors of 2010. you're gifted in more ways than you can imagine. embrace that.. you can do anything you want in your life. be proud of yourselves. i hope for the best for everyone and i'll remember you everytime i walk the halls of riverside academy.
To my seniors: I love you guys more than you know. Every last one of you. Including Mher, although he always seems to not be in class. Yall had an awesome year, I can tell. I hope my senior years proves to be just as great. You guys will be missed, EXTREMELY. especially those of you who have been at RA since I first walked in the front door when I was 4. I always looked up to you guys... cuz yall were older :) and it's so weird to think that next year, we will be the role models. It still hasn't hit me yet.
To my juniors: Well, what can I say. it's been one heck of a ride.. From preschool, to middle school, to soon-to-be seniors. The five of you in the calc class are the people I am most close to out of the ENTIRE jr class. because I spend 90% of my day with you mon-fri... on weekends @ math trips, and during the summer @ practices. I love yall more than you can imagine. I can't wait for next year's calc BC class, it will be fun with just the six of us :)
So i'll stop being all mushy for a moment and talk about calc this year.
Most helpful thing: working in groups at the end of year to go over what you missed on the practice ap tests. one-on-one with another student that will actually make you do your work (thanks ellie) helped me more than you can understand. best idea yet B-ROB.
Thing i struggled with most: integration. i honestly still am not 100% with it, idk what it is. substitution, ln, tan inverse. none of it came to me easily. more practice was needed probably? idk.
Thing I picked up on the quickest: the derivative formulas. I can still say them to you probably quicker than anyone in the class. all those derivative practice sheets in the beginning were SOOOO helpful.
My epiphany of the year: the riemann sum formulas!!!!!!!!! honestly, i didn't understand all that f(a) + f(2 + a) stuff. and multiply by delta x whatever. it must easier when taught that TRAM is
b' + b'' / 2 (n) + b'' + b''' /2 (n). also the LRAM and RRAM are easier when taught that you add to x's divide by n (start all the way to left with LRAM and 2nd number with RRAM). that literally clicked in my head 2 days before the exam.
so, even though I don't want it to, this year is coming to a close. and quick too. I'm going to miss all you entirely too much. I will probably cry... a lot. just because I'm about to be a senior. i'll be sad everyday in calculus when i realize how small the class is. (& when i realize that mher IS actually not there). we had a great year, from partying it up with mr. st pierre to re-partying it up with brob. & of course getting people to sneak out of school to buy us some soft drinks because ricky never brings his stuff! i will miss it all.
GOOD LUCK TO YOU, seniors of 2010. you're gifted in more ways than you can imagine. embrace that.. you can do anything you want in your life. be proud of yourselves. i hope for the best for everyone and i'll remember you everytime i walk the halls of riverside academy.
Stephanie's Final Blog
As this year comes to a close, I'd like to tell everyone how great our class was this year. Especially with our mad covert partying skills, our ability to goof off and still get our work done, and lastly, our great personalities. The seniors this year are great, and i'll miss every one of yall. To my juniors, LETS GET THIS PARTY STARTED. I'm ready to own the school, yall bout it?
So, something i couldn't understand then it just smoked me in the face is substitution. I think it took Ryan Breaud just yelling at me about how to substitute, then somehow making it involve either a mean girl quote, bonquiqui, or darrel, spelt like darrel, but pronounced like darrel. I can't explain how it really stuck in my head besides taht. But give me something today, and i'll substitute the numbers out of it. Watch out.
This was definately one of my favorite classes this year, besides the MASSIVE struggles i've had in this class, it definately taught me that i can achieve what I strive to do. And to the seniors leaving, i'm glad i got to take this class with yall, and yall better remember the good times we had..and if anyone gets famous remember the girl who mission impossibled it to the cafeteria to get ice for our cups.
To the juniors, well seniors now, lets make this year the greatest ever. I mean i'm already great, and yall have class with me, so that makes you offliated with greatness, which means you're semi-great..and so add that together, then you get that we're all great. because of me, of course. :)
Also, thanks to Mrs. Robinson for helping me this year and not giving up on me when i answer free response questions without thinking. I know i couldn't of done it with out you.
Lastly, i have to tell everyone thanks for making my first hour great, and you better not ever forget me. :)
So, something i couldn't understand then it just smoked me in the face is substitution. I think it took Ryan Breaud just yelling at me about how to substitute, then somehow making it involve either a mean girl quote, bonquiqui, or darrel, spelt like darrel, but pronounced like darrel. I can't explain how it really stuck in my head besides taht. But give me something today, and i'll substitute the numbers out of it. Watch out.
This was definately one of my favorite classes this year, besides the MASSIVE struggles i've had in this class, it definately taught me that i can achieve what I strive to do. And to the seniors leaving, i'm glad i got to take this class with yall, and yall better remember the good times we had..and if anyone gets famous remember the girl who mission impossibled it to the cafeteria to get ice for our cups.
To the juniors, well seniors now, lets make this year the greatest ever. I mean i'm already great, and yall have class with me, so that makes you offliated with greatness, which means you're semi-great..and so add that together, then you get that we're all great. because of me, of course. :)
Also, thanks to Mrs. Robinson for helping me this year and not giving up on me when i answer free response questions without thinking. I know i couldn't of done it with out you.
Lastly, i have to tell everyone thanks for making my first hour great, and you better not ever forget me. :)
Ellie's Final Reflection
Alright you guys!!! We've gotten through calculus and we've all made it. When this class first started, I wasn't stressed out by the least. Having a teacher like Mrs. Robinson the year before, I knew what I was getting into. The first week was oddly enough, expected! We got so many formulas to memorize and so many ways of taking a derivative a lot of us were going crazy, but not me, I was kind of like "whatever" with it. Turns out two or three weeks into it, I got really scared, my grades weren't really slipping but I wasn't getting the new, or harder, derivatives. After that, I buckled down and got to work. Here's what I've learned throughout the year...
Easy Concepts For Me:
--How to Take a Derivative:
You take the exponent and times it by the coefficient, what you get is the new coefficient and you're new exponent will be the original exponent minus one!
--The First Derivative Test:
You have to take the derivative of the function and set it equal to zero. Then solve for the critical values (x values). Set those values up into intervals between negative infinity and infinity. Plug in numbers between these intervals into the first derivative to see if there are max or mins or if the graph is increasing or decreasing.
--The Second Derivative Test:
You take the derivative of the function twice and set it equal to zero. Solve for the x values and set them up into intervals between negative infinity and infinity. Plug in numbers between those intervals into the second derivative to see where the graph is concave up, concave down, or where there is a point of inflection.
--Maximums, minimums, critical values, increasing, decreasing:
All of these are related to first derivative test. it's simple. you take the derivative, set equal to 0, solve for x. Set up some intervals using these numbers. Plug in numbers and test your intervals. pos to neg is a min. neg to pos is a max. pos = increasing, neg = decreasing. simple stuff. remember it.
--Point of inflection, concave up, concave down:
It's the second derivative test. set up intervals, if the intervals change signs, it is a point of inflection there. also, if its negative, that interval is concave down, positive is concave up.
--Finding Critical Values:
To find critical values, first take the derivative of the function and set it equal to zero, solve for x. The answers you get for x are your critical values.
--Limits:
If the degree on top is smaller than the degree on the bottom, the limit is zero.
If the degree on top is bigger than the degree on the bottom, the limit is infinity.
If the degree on top is the same as the degree on the bottom, you divide the coefficients to get the limit.
Some Concepts that...after reviewing over and over for weeks/months...it just clicked:
--Slope of a normal line:
Take derivative, plug in x. get a slope. however, make sure you use the negative reciprocal of the slope (normal means perpendicular to). use point-slope formula.
--Absolute Extrema:
If you are given a point, plug those numbers into the original function to get another number. Alos, solve for critical values and plug those into the original function. Once you get your second numbers, you set each pair into new sets of points. The highest point is the absolute max and the smallest point is the absolute min.
--Average Rate of Change:
f(b)-f(a)/(b-a)
--Average Value:
This is just an integral times by 1/(b-a).
--Equation of a Tangent Line:
Take the derivative and plug in the x value.
If you are not given a y value, plug into the original equation to get the y value.
then plug those numbers into point slope form: y − y1 = m(x − x1)
And-of course-the things that I always struggled with, and hope to never encounter again even though I know I will....:
--linearization:
Identify the equation
Use the formula f(x)+f ' (x)dx
Determine your dx in the problem
Then determine your x in the problem
Plug in everything you get
Solve the equation
--Riemanns Sums:
LRAM-Left hand approximation=delta x[f(a)+f(a+delta x)+...f(b-delta x)]
RRAM-Right hand approximation=delta x[f(a+delta x)+...f(b)]
MRAM-Middle approximation=delta x[f(mid)+f(mid)+...]
Trapezoidal-delta x/2[f(a)+2f(a+delta x)+2f(a+2 delta x)+...f(b)]
delta x=b-a/number of subintervals
--Volume by Disks:The formula is pi times the integral of the [function given] squared times dx. so just solve it by taking the integral of it and then pluging in the numbers they give you. just like before you'll have two numbers so whatever the answer is for the top one will be first and then you subtract the answer you get for the bottom one. then graph
--Volume by Washers:
The formla is pie times the integral of the [top function] squared minus the [bottom function] squared times dx. so to do this, if you don't have the in between number you have to set the functions equal, but if you do, then it's worked the same way as above. square the formula's that were given and simplify. then take the integral of it and plug in the numbers they give you or you found by setting the formulas equal to each other and then solve like any other one by subracting them. then graph.
--OPTIMIZATION...
I just can't do it =(
Just a shout out:
To the seniors in the Calculus Class of 2010 - - I'll Miss Yall, we've grown up together basically. I won't lie, I didn't like MANY of yall when I first came here because of different things that happened; however, we've all matured [thank God] and we've become friends. Although some of us aren't best friends I can honestly say that I will miss each and every one of you all because yall are the people I spent all day every day with for the past 6 years.
To the juniors in the Calculus Class of 2010 - - I'll miss yall just as much. There's many reason's why I will..some were my first friend at Riverside Academy because of the Cheerleading Squad, some have always been in my life because we grew up living next door to each other, some have been with me through the years with dancing and just being friends, some HOWEVER have become my friend in this past year and believe me I love yall just as much!
So back to the FARWELLS:
No, I'm not sad I'm graduating. My parents say that it hasn't hit me yet...but most of yall know me already and I'm so happy to finally be just about OUT of Riverside Academy that nothing else matters. Also, I'm not sad that I'm leaving any of yall. Yall have been great friends and I'm glad we've become as close as we have or, not as close as we have in some cases, because LIFE GOES ON..We cannot dwell in the past much less live it. I won't be back at Riverside once I'm out, there's no need....I'm finally getting my life started and I CAN'T WAIT!! =) Yeah, I'll miss yall when certain things come up and I realize what [so and so] would've said and they wont be there..but most of all .. I'll miss US as a class together and how we are with each other! So to everyone - - THANKS! And have a GREAT time either being a senior, or going out into the REAL WORLD and EXPERIENCING everything!
Love Always,
Ellie Kliebert
Easy Concepts For Me:
--How to Take a Derivative:
You take the exponent and times it by the coefficient, what you get is the new coefficient and you're new exponent will be the original exponent minus one!
--The First Derivative Test:
You have to take the derivative of the function and set it equal to zero. Then solve for the critical values (x values). Set those values up into intervals between negative infinity and infinity. Plug in numbers between these intervals into the first derivative to see if there are max or mins or if the graph is increasing or decreasing.
--The Second Derivative Test:
You take the derivative of the function twice and set it equal to zero. Solve for the x values and set them up into intervals between negative infinity and infinity. Plug in numbers between those intervals into the second derivative to see where the graph is concave up, concave down, or where there is a point of inflection.
--Maximums, minimums, critical values, increasing, decreasing:
All of these are related to first derivative test. it's simple. you take the derivative, set equal to 0, solve for x. Set up some intervals using these numbers. Plug in numbers and test your intervals. pos to neg is a min. neg to pos is a max. pos = increasing, neg = decreasing. simple stuff. remember it.
--Point of inflection, concave up, concave down:
It's the second derivative test. set up intervals, if the intervals change signs, it is a point of inflection there. also, if its negative, that interval is concave down, positive is concave up.
--Finding Critical Values:
To find critical values, first take the derivative of the function and set it equal to zero, solve for x. The answers you get for x are your critical values.
--Limits:
If the degree on top is smaller than the degree on the bottom, the limit is zero.
If the degree on top is bigger than the degree on the bottom, the limit is infinity.
If the degree on top is the same as the degree on the bottom, you divide the coefficients to get the limit.
Some Concepts that...after reviewing over and over for weeks/months...it just clicked:
--Slope of a normal line:
Take derivative, plug in x. get a slope. however, make sure you use the negative reciprocal of the slope (normal means perpendicular to). use point-slope formula.
--Absolute Extrema:
If you are given a point, plug those numbers into the original function to get another number. Alos, solve for critical values and plug those into the original function. Once you get your second numbers, you set each pair into new sets of points. The highest point is the absolute max and the smallest point is the absolute min.
--Average Rate of Change:
f(b)-f(a)/(b-a)
--Average Value:
This is just an integral times by 1/(b-a).
--Equation of a Tangent Line:
Take the derivative and plug in the x value.
If you are not given a y value, plug into the original equation to get the y value.
then plug those numbers into point slope form: y − y1 = m(x − x1)
And-of course-the things that I always struggled with, and hope to never encounter again even though I know I will....:
--linearization:
Identify the equation
Use the formula f(x)+f ' (x)dx
Determine your dx in the problem
Then determine your x in the problem
Plug in everything you get
Solve the equation
--Riemanns Sums:
LRAM-Left hand approximation=delta x[f(a)+f(a+delta x)+...f(b-delta x)]
RRAM-Right hand approximation=delta x[f(a+delta x)+...f(b)]
MRAM-Middle approximation=delta x[f(mid)+f(mid)+...]
Trapezoidal-delta x/2[f(a)+2f(a+delta x)+2f(a+2 delta x)+...f(b)]
delta x=b-a/number of subintervals
--Volume by Disks:The formula is pi times the integral of the [function given] squared times dx. so just solve it by taking the integral of it and then pluging in the numbers they give you. just like before you'll have two numbers so whatever the answer is for the top one will be first and then you subtract the answer you get for the bottom one. then graph
--Volume by Washers:
The formla is pie times the integral of the [top function] squared minus the [bottom function] squared times dx. so to do this, if you don't have the in between number you have to set the functions equal, but if you do, then it's worked the same way as above. square the formula's that were given and simplify. then take the integral of it and plug in the numbers they give you or you found by setting the formulas equal to each other and then solve like any other one by subracting them. then graph.
--OPTIMIZATION...
I just can't do it =(
Just a shout out:
To the seniors in the Calculus Class of 2010 - - I'll Miss Yall, we've grown up together basically. I won't lie, I didn't like MANY of yall when I first came here because of different things that happened; however, we've all matured [thank God] and we've become friends. Although some of us aren't best friends I can honestly say that I will miss each and every one of you all because yall are the people I spent all day every day with for the past 6 years.
To the juniors in the Calculus Class of 2010 - - I'll miss yall just as much. There's many reason's why I will..some were my first friend at Riverside Academy because of the Cheerleading Squad, some have always been in my life because we grew up living next door to each other, some have been with me through the years with dancing and just being friends, some HOWEVER have become my friend in this past year and believe me I love yall just as much!
So back to the FARWELLS:
No, I'm not sad I'm graduating. My parents say that it hasn't hit me yet...but most of yall know me already and I'm so happy to finally be just about OUT of Riverside Academy that nothing else matters. Also, I'm not sad that I'm leaving any of yall. Yall have been great friends and I'm glad we've become as close as we have or, not as close as we have in some cases, because LIFE GOES ON..We cannot dwell in the past much less live it. I won't be back at Riverside once I'm out, there's no need....I'm finally getting my life started and I CAN'T WAIT!! =) Yeah, I'll miss yall when certain things come up and I realize what [so and so] would've said and they wont be there..but most of all .. I'll miss US as a class together and how we are with each other! So to everyone - - THANKS! And have a GREAT time either being a senior, or going out into the REAL WORLD and EXPERIENCING everything!
Love Always,
Ellie Kliebert
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