Yeah I realized I didn't post questions too! But I really do have questions. Maybe someone can answer these if they haven't done their comments..since no really did questions.
1. Like how you tell when it is divergent or convergent?
2. For improper integrals, sometimes they don't have an infinity so how do you break it up?
3. I need a reminder for how to do chasing the rabbit!
4. And how do you integrate 14x^27 cosx^14 dx?
Thursday, October 7, 2010
Wednesday, October 6, 2010
No Questions.
Since there are no questions on anyone's blogs. I'll just do a mini-blog.
INTEGRATION:
Anytime there is an x term and an e term in a problem, use by-parts. The x term will always be your u and the e term will always be the dv.
Anytime there is an e term and a trig term, use by-parts until you see chasing the rabbit.
Anytime there is an x term and a trig term, use by-parts with your u as the x.
Questions:
S x^2 / x+3 I have no clue how to even start this.
This is from Calc. 1, but can anyone tell me the difference between a washer and (I don't know the other thing). THANKS
ryan
INTEGRATION:
Anytime there is an x term and an e term in a problem, use by-parts. The x term will always be your u and the e term will always be the dv.
Anytime there is an e term and a trig term, use by-parts until you see chasing the rabbit.
Anytime there is an x term and a trig term, use by-parts with your u as the x.
Questions:
S x^2 / x+3 I have no clue how to even start this.
This is from Calc. 1, but can anyone tell me the difference between a washer and (I don't know the other thing). THANKS
ryan
sorry
no one posted questions on their blogs. that's why i don't have comments. NEXT TIME, please post questions :)
Monday, October 4, 2010
Post...
Just some throwback steps straight from my old notebook. thought they MIGHT be useful to some...
First Derivative Test:
1. Take the derivative of the original problem.
2. Set the first derivative equal to Zero.
3. Solve for x.
4. Create intervals for x. i.e. (-∞, 1) (1, 4) (4, ∞)
5. Pick a number in the intervals then plug that number in the first derivative for x.
6. Solve.
Second Derivative Test:
1. Take the derivative of the first derivative.
2. Set the second derivative equal to Zero.
3. Solve for x.
4. Create intervals for x. i.e. (-∞, 1) (1, 4) (4, ∞)
5. Pick a number in the intervals then plug that number in the second derivative for x.
6. Solve.
limits:
Rule #1 - When the degree (exponent) of the bottom is GREATER than the degree of the top, the limit is Zero.
Rule #2 - When the degree (exponent) of the bottom is SMALLER than the degree of the top, the limit is infinity. (positive or negative)
Rule #3 - When the degrees are equal, the limit is the coeffecients.
linierazation:
The steps for solving linearization problems are:
1. Pick out the equation
2. f(x)+f`(x)dx
3. Figure out your dx
4. Figure out your x
5. Plug in everything you get
implicit derivatives:
First Derivative:
1. take the derivative of both sides
2. everytime you take the derivative of y note it with dy/dx or y^1
3. solve for dy/dx
Second Derivative:
first you find the first derivative and solve it for dy/dx by using the steps for the first derivative steps.
you then take the second derivative of the solved equation. Plugging in d^2y/d^2x everytime you take the derivative of y again. and where you have dy/dx you plug in your solved equation for that.
once you have everything plugged in and ready to go you then solve for d^2y/d^2x
HOW TO FIND THE EQUATION OF A TANGENT LINE:
1. take f'(x)
2. plug x in to find your slope m
3. plug x into f(x)to get y
4. using m and (x,y) plug it into the equation (y-y1)=m(x-x1).
First Derivative Test:
1. Take the derivative of the original problem.
2. Set the first derivative equal to Zero.
3. Solve for x.
4. Create intervals for x. i.e. (-∞, 1) (1, 4) (4, ∞)
5. Pick a number in the intervals then plug that number in the first derivative for x.
6. Solve.
Second Derivative Test:
1. Take the derivative of the first derivative.
2. Set the second derivative equal to Zero.
3. Solve for x.
4. Create intervals for x. i.e. (-∞, 1) (1, 4) (4, ∞)
5. Pick a number in the intervals then plug that number in the second derivative for x.
6. Solve.
limits:
Rule #1 - When the degree (exponent) of the bottom is GREATER than the degree of the top, the limit is Zero.
Rule #2 - When the degree (exponent) of the bottom is SMALLER than the degree of the top, the limit is infinity. (positive or negative)
Rule #3 - When the degrees are equal, the limit is the coeffecients.
linierazation:
The steps for solving linearization problems are:
1. Pick out the equation
2. f(x)+f`(x)dx
3. Figure out your dx
4. Figure out your x
5. Plug in everything you get
implicit derivatives:
First Derivative:
1. take the derivative of both sides
2. everytime you take the derivative of y note it with dy/dx or y^1
3. solve for dy/dx
Second Derivative:
first you find the first derivative and solve it for dy/dx by using the steps for the first derivative steps.
you then take the second derivative of the solved equation. Plugging in d^2y/d^2x everytime you take the derivative of y again. and where you have dy/dx you plug in your solved equation for that.
once you have everything plugged in and ready to go you then solve for d^2y/d^2x
HOW TO FIND THE EQUATION OF A TANGENT LINE:
1. take f'(x)
2. plug x in to find your slope m
3. plug x into f(x)to get y
4. using m and (x,y) plug it into the equation (y-y1)=m(x-x1).
Post #6
Rules for Limits if x--->infinity
1. degree of top equals degree of bottom-->ANSWER: top coefficient over bottom coefficient
2. degree is bigger than bottom degree-->ANSWER: positive or negative infinity
3. top degree is less than bottom degree-->ANSWER: 0
Also with limits--->if indeterminate form is created
L'Rule! All you do is take derivative of top over derivative of bottome. If indeterminate form is still created then simply repeat.
NOTE: I have been getting a lot better at substitution. With all the practice I'm starting to recognize things that need to be substituted. Like if you have sin and cos, those are derivatives of each other so you would use substitution.
NOTE: Let's not forget that the integrals of some things are on our chart. Most of them are like ln of something.
NOTE: Remember AREA means to INTEGRATE! I saw that one popped up on the packet.
1. degree of top equals degree of bottom-->ANSWER: top coefficient over bottom coefficient
2. degree is bigger than bottom degree-->ANSWER: positive or negative infinity
3. top degree is less than bottom degree-->ANSWER: 0
Also with limits--->if indeterminate form is created
L'Rule! All you do is take derivative of top over derivative of bottome. If indeterminate form is still created then simply repeat.
NOTE: I have been getting a lot better at substitution. With all the practice I'm starting to recognize things that need to be substituted. Like if you have sin and cos, those are derivatives of each other so you would use substitution.
NOTE: Let's not forget that the integrals of some things are on our chart. Most of them are like ln of something.
NOTE: Remember AREA means to INTEGRATE! I saw that one popped up on the packet.
Sunday, October 3, 2010
post 6
l'hospitals rule:
if the limit is in indeterminate form, you use this.
you take the derivative of the top and the bottom of the fraction (separately, do not use quotient rule) and then take the limit of it again.
if you get indeterminate form, repeat as many times as necessary.
this week in calc, we just went over all the ways to integrate pretty much. partial fractions, trig sub, all that good stuff. and we had a test on thursday. and now we have a take home test due this week sometime (i think either thursday/friday) if someone knows when it is due please tell me.
i'm just gonna kinda review randomness today.
sorry if it's short. i'm not really focused too well right now...
partial fractions:
whenever you simplify the bottom of the fraction as much as you can... if you have something like this n/n(n-1)
you'd use the normal rules and just do A/n + B/n-1.
but if you ever have something left in the bottom that is still squared, that's when the rules get tricky.
if your exponent is on the outside of the equation...(example: x/(x-1)^2) then you would do A/(x-1) + B/(x-1)^2
and if your exponent was 7, then you would go all the way up to 7.
no if your exponent is on the inside of the equation....(x/(x^2-1) then you would do like this... A + Bx/(x^2-1)
get it ? hopefully you do.
now i am confused on what convergent and divergent is and how you can tell the difference.
help?
if the limit is in indeterminate form, you use this.
you take the derivative of the top and the bottom of the fraction (separately, do not use quotient rule) and then take the limit of it again.
if you get indeterminate form, repeat as many times as necessary.
this week in calc, we just went over all the ways to integrate pretty much. partial fractions, trig sub, all that good stuff. and we had a test on thursday. and now we have a take home test due this week sometime (i think either thursday/friday) if someone knows when it is due please tell me.
i'm just gonna kinda review randomness today.
sorry if it's short. i'm not really focused too well right now...
partial fractions:
whenever you simplify the bottom of the fraction as much as you can... if you have something like this n/n(n-1)
you'd use the normal rules and just do A/n + B/n-1.
but if you ever have something left in the bottom that is still squared, that's when the rules get tricky.
if your exponent is on the outside of the equation...(example: x/(x-1)^2) then you would do A/(x-1) + B/(x-1)^2
and if your exponent was 7, then you would go all the way up to 7.
no if your exponent is on the inside of the equation....(x/(x^2-1) then you would do like this... A + Bx/(x^2-1)
get it ? hopefully you do.
now i am confused on what convergent and divergent is and how you can tell the difference.
help?
Post # 6
So, lets go through a few throwback/ things that are necessary to be known. This week we prepared for the test and hopefully we all did good on it! Cross your fingers being that exams are coming up shortly!! Ahh, deep breath. So, anyway, I'm going to go over a few things that need to be remembered because they are in all of the parts of what we've been up to..so here it goes…
SUBSTITUTION
Substitution takes the place of the derivative rules for problems such as product rule and quotient rule and should be used PLENTY right now…
The steps to substitution are:
1. Find a derivative inside the interval
2. set u = the non-derivative
3. take the derivative of u
4. substitute back in
e INTEGRATION
- whatever is raised to the e power will be your u, and du will be the derivative of u.
For example:
e^2x-1dxu=2x-1 du=2
rewrite the function as:
1/2{ e^u du, therefore
= 1/2e^2x-1+C is your final answer.
LIMITS:
Rules for Limits:…
1. if the degree of top equals the degree of bottom, the answer is the top coefficient over bottom coefficient
2. if top degree is bigger than bottom degree, the answer is positive or negative infinity
3. if top degree is less than bottom degree, the answer is 0
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