Twelfth week of calculus. Monday-Study Tuesday-Study Wednesday-Test Thursday-Test Friday-LEARN!
Our test was on everything we did this whole year. I actually understand a lot of things now that we reviewed for everything for two days. The things I didn't understand on the test were just the formulas. I knew how to work all the related rates and angle of elevation problems but I couldn't remember any of the formulas.But I finally did learn them, so here they are.
CONE- V=3/4(pi)(h)(r^2)
CUBE- V=E^3
RECTANGLE- A=1/2(B)(H)
SQUARE- A=L x W P=2(L+W)
SPHER- V=1/3(pi)(r^3)
CIRCLE- A=2(pi)(r)
how to find a tangent line:
1. Take derivative
2. Plug x in to derivative to find slope
3. Plug slope into original to find y-intercepts
4. plug in slope and point into the equation (y-y1)=m(x-x1).
I don't really understand linearization. Well, i really just dont remember it. Because we didn't have that much practice, but hopefully we'll be going over it next week. If anyone did understand it please refresh my memory.
I don't really understand linearization. Well, i really just dont remember it. Because we didn't have that much practice, but hopefully we'll be going over it next week. If anyone did understand it please refresh my memory.
Linearization
ReplyDeleteany time we see the word APPROXIMATE we will be using linerarization.
For example:
Approximate the tangent line to y=(x)^2 at x=5
that means that dy/dx is 2x
so when we plug in 5 for x we get 2(5) which is 10. 10 is our slope!. Now we will take the original and plug in 5 for x giving us y=(5)^2, so that's y=25.
Since the equation for Linerarization is f(x) = f(c) + f'(c)*(x-c) we will plug in what we have into the equation. we know that f(c)=25...f'(c)=2...and c=5 so when we plug in we get>>>> f(x)=25+2(x-5)