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32 Cards in this Set
 Front
 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/(ba) * [antideriv from a to b of f(x)]


[tan(x)]^2 + 1

[sec(x)]^2


linearization

f(a)  [f ' (a) * (x  a)]


halflife

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(1x^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(1x^2)]


antideriv: ln(x)

x  (x)ln(x)


deriv: [sec(x)]^1

1/[abs(x)][root(1x^2)]


deriv: [csc(x)]^1

1/[abs(x)][root(1x^2)]


deriv: sec(x)

sec(x)*tan(x)


deriv: ln(x)

1/x


deriv: csc(x)

csc(x) * cot(x)
