Post #2

the second week of calculus has come to a close. I understand the simeple concepts of the derivitives like the quotient rule vu^1-uv^1/v^2 and the product rule uv^1 + vu^1 and i even understand the sin, cos, tan, etc. rules as well. My biggest problem is that when you have a big problem and you have to do multiple derivitives i get a little lost. For example one problem says ln 3square root x-1/x+1. My first thought would be to treat it as a natural log 1/u X u^1. So i would make it look like 1/(x-1/x+2)^1/3. but i don't understand what u^1 would be or if i need to look at it some other way.

Another one i didn't really understand was -square root of x^2 +4 /2x^2 - 1/4 ln (2+ square root of x^2 +4/x). So i see from looking at it, it is the quotient rule and there is a square root so you have to make it into a fraction.. what confuses me if when i get to the ln part. Simplifying this was also very hard and i catch trouble with that as well. I just need some help breaking down the problem and looking at everything that needs to be done. I know the formulas and how to set them up, i just don't know exactly when to set them up, if that makes any sense.

Other than that, i have a good grasp on the limit stuff and the vertical and horizontal asymptotes for the test wednesday, i just need some help going over the big derivitive problems before we take the test. The only other thing about derivitives that i don't have a big grasp on yet is the e problems. y= e^x-e^-x/2. I see that the quotient rule is here but i don't know what needs to be done with the e's.

I think i will have a handle on the derivitives once someone helps me understand how to break down the problems and know everything that needs to be done in the problem. So all in all, my second week of calculus was not too bad, but i'm just a little confused at times.

Post #2

So it's finally the end of week number two of school, and of Calculus. I won't even joke with you guys, I've been completely lost at some point during this week. I think I'm pretty set on all the different derivatives now. The most important thing that I continue to screw up though, however, is when there is a lot of canceling out to do. I tend to be lazy and try to find shortcuts in skipping steps but it ends up biting me in the behind anyway. :-(

So, things that completely confused me until Thursday...

When you take the derivative of uⁿ it is nu^n-1. Well, I didn't realize that say you have...
(x²-1)² you actually have to use the formula nx^n-1 times u'. So you get 2(x²-1)(2x) so ultimately we get 4x(x²-1).
Hope everyone remembers to do this...

After realizing that every single derivative so far that we've had is times by u' I don't think this will be hard to remember.

Anyway, I think that the test on Wednesday will be really hard...I know it covers limits so I figured I'd help everyone out.

When you take the limit as x goes to infinity, the rules are as follows
1) If the degree of the top is larger than the degree of the bottom, its infinity.
2) If the degree of the top is equal to the degree of the bottom, it is the leading coefficient of the bottom divided by the leading coefficient of the bottom.
3) If the degree of the top is smaller than the degree of the bottom, it is 0.

Other things include vertical asymptotes. To do this, you set the bottom part of the fraction equal to 0. Asymptotes occur at these x-values.

Horizontal Asymptotes follow the rules of limits. (the 1-3 of above). The asymptotes will either not occur (rule 1), at y=coeffi/coeffi (rule 2) or at y=0 (rule 3).

I won't explain them here but don't forget to study removeables, jumps, and infinite discontinuities :-p.

POST #2

OH MY GOSH...THE SECOND WEEK OF CALCULUS IS OVER WITH...

well...i can honestly say that i just cannot grasp the concept of the whole thing. I understand the derivatives, and velocity, and i'm even getting the hang of it in Mu Alpha Theta. But this week in Calculus, it just didn't click.
So monday, was good, IT WAS A REVIEW DAY!...but then tuesday came [well i wasn't in class because i was absent] and when i got the notes, i was completely lost and couldn't do my homework. I sat down for hours to try and figure it out. I'm totally confused on what to do for arccos and arcsin. I know that i got the examples, but once i get to a problem i just freak out i guess. how would you do sin(arccos t) ????
Wednesday-Friday we reviewed from the beginning and even from Advanced Math and of course we had to use BASIC algebra, which seems soo hard because we never had to do THAT much algebra at once. We reviewed logs and exponets. I understood logs, like to find x when you have log2(1/8) you'll take the 2 and put the x as it's exponet and solve for x when it's set equal to (1/8). It'll give you -3!!
Hopefully I'm doing that right!
Then the determinates come back again when we have y=4 x
_{...it's the ULNA!..ha
And now i'm on this weekends homework and i'm already having trouble. I think it's the "basic" algebra that's killing me. I'M NOT SURE ON EXACTLY HOW TO START the problemS.
Oh and don't forget that we have a test Wednesday!...i'm scared!}

post #2

Okay so the second week of calculus has past and it's getting better. I'm starting to understand derivatives alot more and both product and quotient rules. All the homework sheets have really helped me to understand the various types of complications one can come across in product and quotient rule problems. I have also learned that some of these problems are really ugly and that you can not cancel out everything if all the sides dont have something in common.


One problem I had trouble with was..y=ln(x(sqrt)x^2-1))..but thankfully mrs.robinson did it on the board and i got it. It's to messy to type it in this blog but the answer after its worked out is (2x^2-1)(x(sqrt.)x^2-1) all over (sqrt of x^2-1). But not everything was messy most of the natural logs were pretty easy. For example, ln2/3= ln^2-ln^3. So basically, its not that bad like i thought it would be. Thanks alot to milky who helped me to understand how to not be confused by all the numbers everywhere on some of the problems on homework. Oh, and listing the rules and stuff before you do the problem makes it so much easier. b-rob helped me alot when she recommended that because it really works for me. Just listing the simple stuff like the exponent rule, the inside exponent, and quotient rule makes it so much easier to work with! and also with a big problem, dont forget to work from the outside-in.

CONFUSED!

i really don't know why...but i just can't seem to get the homework at all ever since i've been absent..

its okay at the beginning but once A LOT of algebra is involved..i'm not sure what to do!

Homework

For number 44 and 45 I'm a little confused.

The arcsec formula what exactly is this IuI ?
Also, how do you solve arctan(x/a)?

Can someone help?

#'s 52-60 on homework

once i hit number 52 i was completely lost.. can someone explain what the steps are in how about doing these problems because i don't even know where to start. Thanks :)

what did we do today in Calc & MAO?

sorry i missed class today [i didn't want to but with 103 fever i kinda couldn't go to school]
but i did go to the doctor so hopefully it helps...

i don't want to be lost when i get back [whenever that is] so please let me know what i missed!
THANKS!
ellie

#73-80 on homework of 8/24

I was doing fine until I got to these problems. I don't know if I over-mathed myself or if I'm just super slow. I completely lost where I was going with any of them. I even lost how to begin. I can't even get to where Kait got. Can someone re-explain how to do one of those problems in simple terms? Please and thank you!!

can anyone help me?

in the homework we had tonight, i thought i was doing them right until i got to 73-76. i worked a few and forgot to put everything over bottom squared while doing the product rule, and i don't know how to work it when i do that. for example in number 73i got x^2 - 2x all over (x - 1)^2. i factored an x out of the top and got x (x-2) all over (x-1)^2. How do i set all of that equal to zero and then solve to find the point(s) of the horizontal tangent line?