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cos(x)

Derivative: sin(x)

-sin(x)

Derivative: cos(x)

sec²(x)

Derivative: tan(x)

-csc(x)cot(x)

Derivative of csc(x)

sec(x)tan(x)

Derivative: sec(x)

-csc²(x)

d/dx cot(x)

1/√(1-x²)

Derivative: sin⁻¹(x)

-1/√(1-x²)

Derivative: cos⁻¹(x)

1/(1+x²)

Derivative: tan⁻¹(x)

-1/(1+x²)

Derivative: cot⁻¹(x)

1/(x√(x²-1))

Derivative: sec⁻¹(x)

-1/(x√(x²-1))

Derivative: csc⁻¹(x)

1/ƒ'(y)

Derivative: ƒ⁻¹(x)

y'

Derivative: y

Horizontal Tangent Line

The tangent line to a point where ƒ'(x)=0

Vertical Tangent Line

the tangent line to a point where ƒ'(x) fails to exist

(dV/dt) = 2πr(dr/dt)h + πr²(dh/dt)

The derivative of V = πr²h with respect to time

csc(x)=

1/sin(x)

sec(x)=

1/cos(x)

tan(x)=

sin(x)/cos(x)

cot(x)=

cos(x)/sin(x)

V=(4/3)πr³

Volume of a Sphere

V=πr²h

Volume of a Circular Cylinder

V=(1/3)πr²h

Volume of a Circular Cone

they are similar triangles with equal proportions

The relationship between an amount in a cone and the dimensions of the cone is

SA=6x²

The Surface Area of a Cube

SA=4πr²

Surface Area of a Sphere

SA=2πr² + 2πrh

The Surface Area of a Cylinder w/Top and Bottom

Max and Min Values live where

The first derivative equals zero or FTE

C=2πr

Circle (circumference)

A=πr²

Area formula with radius

The graph is above the x-axis

If given the graph of a function, the function is positive when

Points of Inflection

The max and min on a graph of the derivative are the what of the original function

The slope of ƒ'(x)

A geometric meaning of ƒ''(x)

Geometric series convergence

If |r|<1, the series converges

∑arⁿ⁻¹

Geometric series layout

S=a/(1-r)

Sum of geometric series

Sequence convergence/divergence

Lim(n→∞) aⁿ = L

lim(n→∞) aⁿ⁺¹/aⁿ

What is the ratio test?

Ratio test conditions

If p<1, the series converges

∑(-1)ⁿ⁺¹bⁿ

Alternating series layout

bⁿ>0

Conditions for series convergence