• # Monday, April 11th

Review of stuff we need to know cold! I missed inverse trig derivatives on the timed quiz.
d/dx[arcsinx] = 1/root(1-x^2)
d/dx[arctanx] = 1/(1+x^2)
d/dx[arcsecx] = 1/(abs val(x)root(x^2-1))
Derivatives of the respective cofunctions have -1 in the numerator.
• # Second Fundamental Theorem of Calculus

d/dx [integral from a to x: f(t)dt] = f(x) Important details:
-upper bound must have a different variable from integrand. (but upper bound variable matches function variable on other side)
-if upper bound is a more complex function than x (such as x^2), use the chain rule! (ex: f(x^2) = 2xf(x^2)) ^^I think???
• # Vertical asymptotes

Remember that to find vertical asymptotes, look at end behavior: limits as function approaches infinity and negative infinity. Also look for places where the function does not exist.
• # indeterminate forms

0/0
infinity/infinity
ininity-infinity
0*infinity
1^infinity
0^0
infinity^0 *****ZERO TO THE INFINITY EQUALS ZERO*****
(but one to the infinity is indeterminate!)
• # y=vx : variable change for homog. diffEQs

Dr. Chris Tisdell explains Homogeneous diffEQ is in the form of:
M(x,y)dx + N(x,y)dy = 0, where M and N are homogeneous functions of the same degree. (means f(tx, ty) = t^n*f(x,y))
***Separate the dx and the dy first! ...If diffEQ is homogenous, then you can make the substitution y=vx, which also means that dy = xdv +vdx. This will lead to a separable diffEQ, which you can solve in terms of v and then convert v's back into y/x.
• # things to review...

I'm still uncomfortable with vectors. I need to review displacement, specifically. I also need to review area under a polar curve. I know that the formula is 1/2(integral from alpha to beta of the function squared), but finding the tangent lines where the function and its derivative are zero confuses me.
• # LIPET

For integration by parts, choosing u: Logarithms
Inverse trig
Polynomials
Exponentials
Trig
• # Know your stuff cold!

I know my inverse trig derivatives.
What is Simpson's rule?
• # Day before the exam!

There will only be two non-calculator problems on the free response section. I can do this!