Okay, so i'm just going to kind of explain the things i don't understand..
1. So, let me start with the improper integrals. I dont understand how to plug in certain things to it? or what you do.
2. Will lo'hopitals rule work for all limits?
3. How do you know if a problem with a squareroot should be solved by substitution, bi-parts..etc.
4. What is the best way to solve a limit.
Okay, so lets get to explaining a little.
When you do the thing with the chart on page A21, you should be aware to make sure all of the important things are being substituted for; as well as integrating if it still has an integral symbol in the equation!
Sorry this blog isn't very informative..but it helps me more when poeple answer my questions then saying what i know. Hopefully someone can help!
Monday, September 27, 2010
Sunday, September 26, 2010
Post #5
Well I didn't bring home my notebook...so lets see what I can remember.
I know we talked about how if you have a definite integral with bounds that have an infinity in it. Also does this apply where you have a discontinuity or something? Well, anyways you replace it with an A or some other letter. Then I think you integrate normally..and then take the limit? I actually was confused on this last week. Can anyone give me an example or explain it better?
Well I will reexplain Lo'Hopital's Rule:
This is when you have a limit. You then plug in the number the limit is approaching into the equation. If you get anything like infinity/infinity, zero/zero, infinity/zero, zero/infinity you need Lo'Hopital's rule. So, you take derivative of the top and derivative of the bottom. Plug in the number from the limit. If you still get anything like infinity/infinity..etc. then you repeat this process. If not then you are done!
One last thing:
How do you know when something is to integrate with substitution?
I know we talked about how if you have a definite integral with bounds that have an infinity in it. Also does this apply where you have a discontinuity or something? Well, anyways you replace it with an A or some other letter. Then I think you integrate normally..and then take the limit? I actually was confused on this last week. Can anyone give me an example or explain it better?
Well I will reexplain Lo'Hopital's Rule:
This is when you have a limit. You then plug in the number the limit is approaching into the equation. If you get anything like infinity/infinity, zero/zero, infinity/zero, zero/infinity you need Lo'Hopital's rule. So, you take derivative of the top and derivative of the bottom. Plug in the number from the limit. If you still get anything like infinity/infinity..etc. then you repeat this process. If not then you are done!
One last thing:
How do you know when something is to integrate with substitution?
Week 5 maybe?
Wellllllll, I forgot my notebook at school on friday so I guess I'll just explain some stuff by memory.
Throwbacks from Calculus 1!
Throwback from Calc. 1 that can help us in physics!
Position, Velocity, Acceleration.
Velocity is the derivative of Position.
Acceleration is the derivative of Velocity.
Physics explains it as:
Velocity is how fast an x (position) is moving.
Acceleration is how fast you are going faster.
Calculus is basically an easier way to do this.
Antiderivative = Integration.
Anytime you see instantaneous rate of change, just take a derivative and plug in for x.
Trig Problems:
tancot = 1
cot/csc = cos
sin(2x) = 2sin(x)cos(x)
sin(-x) = -sin(x)
QUESTIONS, I'm looking at a MAO test right now that I have.
Oblique asymptote?
When you have an integral from 0 to x^2 and give you a value and say take the derivative. How you do that?
How to do f^(-1)'(x).
Any Volume problems.
Throwbacks from Calculus 1!
Throwback from Calc. 1 that can help us in physics!
Position, Velocity, Acceleration.
Velocity is the derivative of Position.
Acceleration is the derivative of Velocity.
Physics explains it as:
Velocity is how fast an x (position) is moving.
Acceleration is how fast you are going faster.
Calculus is basically an easier way to do this.
Antiderivative = Integration.
Anytime you see instantaneous rate of change, just take a derivative and plug in for x.
Trig Problems:
tancot = 1
cot/csc = cos
sin(2x) = 2sin(x)cos(x)
sin(-x) = -sin(x)
QUESTIONS, I'm looking at a MAO test right now that I have.
Oblique asymptote?
When you have an integral from 0 to x^2 and give you a value and say take the derivative. How you do that?
How to do f^(-1)'(x).
Any Volume problems.
Mal's Post
Whatever will I explain on this fine evening????
Hmm...good question.
How about some throwback?
Okay, so derivatives...because I'm a little rusty on that.
Okay. So, my thing is that lately I've been noticing that every time I'm trying to take the derivative of my u in py parts, I'm actually integrating. Which isn't what your supposed to be doing. So here's a little review.
a derivative is a what?
SLOPE. Good! I'm glad we're off to a good start here...
Okay. How do you find a slope/derivative?
Well, you multiply the the variable by your exponent and then subtract one from your exponent. VOILA!!! a derivative.
So if I'm given the position equation x(t)=2t^2+5t and I want to find the velocity at t=4, what do I do? Well, I take the derivative of the equation first then plug in 4 to see just what the slope(velocity) is at that particular point. So:
my derivative equals 4t+5. Now you plug in 4.
16+5=21!!!!! Congrats!!! okay.
Now, if I want to find the acceleration, what do I do? take the derivative twice. The second derivative (hence the word twice)..
so we found the first time that it was 4t+5 was the velocity.
so the second derivative would equal what? well the derivative of 5 is 0...constant derivative=0....and the derivative of 4t is just 4...so you acceleration at any point (even t=4, 5, or 6) is 4.
Another quick review would be the following:
If I want to get back from say acceleration to velocity. what would I do? integrate.
Now I realize that I'm being redundant and reviewing probably what's the easiest things in the big mighty calculus book, but I needed SOMETHING to talk about. Love you guys!
Hmm...good question.
How about some throwback?
Okay, so derivatives...because I'm a little rusty on that.
Okay. So, my thing is that lately I've been noticing that every time I'm trying to take the derivative of my u in py parts, I'm actually integrating. Which isn't what your supposed to be doing. So here's a little review.
a derivative is a what?
SLOPE. Good! I'm glad we're off to a good start here...
Okay. How do you find a slope/derivative?
Well, you multiply the the variable by your exponent and then subtract one from your exponent. VOILA!!! a derivative.
So if I'm given the position equation x(t)=2t^2+5t and I want to find the velocity at t=4, what do I do? Well, I take the derivative of the equation first then plug in 4 to see just what the slope(velocity) is at that particular point. So:
my derivative equals 4t+5. Now you plug in 4.
16+5=21!!!!! Congrats!!! okay.
Now, if I want to find the acceleration, what do I do? take the derivative twice. The second derivative (hence the word twice)..
so we found the first time that it was 4t+5 was the velocity.
so the second derivative would equal what? well the derivative of 5 is 0...constant derivative=0....and the derivative of 4t is just 4...so you acceleration at any point (even t=4, 5, or 6) is 4.
Another quick review would be the following:
If I want to get back from say acceleration to velocity. what would I do? integrate.
Now I realize that I'm being redundant and reviewing probably what's the easiest things in the big mighty calculus book, but I needed SOMETHING to talk about. Love you guys!
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