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32 Cards in this Set

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  • Back
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)