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Tyler R.

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Distance Formula

The Mean Value Theorem

If f(x) is

(1) continuous on [a,b]

(2) differentiable on (a,b)

then there exists a number c in (a,b) such that

f'(c)=__f(b) - f(a)__

b - a

(1) continuous on [a,b]

(2) differentiable on (a,b)

then there exists a number c in (a,b) such that

f'(c)=

b - a

or the instantaneous roc = average roc

FTCI

If f(x) is conti on [a, b] then integral from x to a of f(t) is conti on [a, b] and diff on (a, b) & derivative of integral is equal to f(x)

FTCII

if f(x) is conti on [a, b] and F'(x) = f(x) then integral of f(x) from b to a is F(b) - F(a)

Intermediate Value Theorem

If f(x) is conti on [a, b] and k is any number between f(a) and f(b), then there exists at least one number c in [a, b] such that f(c) = k

Extreme Value Theorem

If f is continuous on a closed interval [a,b], then f has both a minimum and a maximum on the interval

Differentiability and continuity

relationship of continuity to integrability

Remember: is f is differentiable at x=c, then limit as x approaches c of f(x) exists

Average rate of change

Average velocity

Instantaneous ROC

Average Value of a Function

Surface Area of Sphere

Surface Area of Cylinder

Surface Area of Box

Surface Area of Cube

Volume of Sphere

Volume of Cylinder

Volume of Cube

Volume of Box

Area of Circle

area of triangle

area of rectangle

area of square

Area of Sectors

Reciprocal Identity

pythagorean identity

Derivative of tan(x)

Derivative of cot(x)

derivative of sec(x)

derivative of csc(x)

d/dx (arcsin(x))

Derivative of arccot(x)

Derivative of b^x

Derivative of log base b (x)

Derivative of ln(x)

How to find inverse of function

Integral of x^-1

Integral of 1/(x+b)

Integral of 1/(kx+b)

Linearization of a function at x = b

Estimate value of f(2.01) given f(2) = 1 and f'(2) = -8

What is signed area?

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