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### 32 Cards in this Set

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 law of exponential change y = y(initial) * e*(kt) [sin(x)]^2 .5-.5cos(2x) limit -- slope of a curve limit as h approaches 0 of --> [f(a+h) - f(a)] / h average value 1/(b-a) * [antideriv from a to b of f(x)] [tan(x)]^2 + 1 [sec(x)]^2 linearization f(a) - [f ' (a) * (x - a)] half-life ln(2)/k optimization draw a picture, write the formula, auxilliary formula, substitute, state boundaries, solve odd function f(-x) = -f(x) deriv: cot(x) -[csc(x)]^2 Hooke's Law F = kx sin(2x) 2*sin(x)*cos(x) deriv: [sin(x)]^-1 1/[root(1-x^2)] even function f(-x) = f(x) dy/dx of a parametric [dy/dt] / [dx/dt] deriv: log sub (a) of (x) 1/[x * ln(a)] log(sub a) of (x) ln (x)/ ln (a) deriv: [tan(x)]^-1 1/(1+x^2) deriv: [cot(x)]^-1 -1/(1+x^2) deriv: tan(x) [sec(x)]^2 [cot(x)]^2+1 [csc(x)]^2 deriv: a^x a^x * ln(a) deriv: e^x e^x antideriv: u^n (where u is any differentiable function of x) [u^(n+1)] / (n+1) [cos(x)]^2 .5+.5cos(2x) deriv: [cos(x)]^-1 -1/[root(1-x^2)] antideriv: ln(x) x - (x)ln(x) deriv: [sec(x)]^-1 1/[abs(x)][root(1-x^2)] deriv: [csc(x)]^-1 -1/[abs(x)][root(1-x^2)] deriv: sec(x) sec(x)*tan(x) deriv: ln(x) 1/x deriv: csc(x) -csc(x) * cot(x)