CALC BC EXAM PREP

  • 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!