Calculus

Theorems

100

This theorem helps you find the limit of a function f(x) with

g(x) ≤ f(x) ≤ h(x)and

lim(x) → a g(x)  =  lim(x) → a h(x)  =  L

Squeeze Theorem

200

if is a continuous function whose domain contains the interval [a, b], then it takes on any given value between and  at some point within the interval

Intermediate Value Theorem

300

If f is continuous on [a,b] and differentiable on (a,b), then there is a point c between a and b so that f'( c ) has the same slope as a line between (a,f(a)) and (b,f(b))

Mean Value Theorem

400

A theorem which provides a technique to evaluate limits of indeterminate forms

L'Hopital's Rule

500

A formula that expresses the derivative of the composition of two differentiable functions f and g in terms of the derivatives of f and g

Chain Rule

Integral Practice

100

This function is the antiderivative of (1+x2)-1.

Tan(x)

200

This function is given by

∫1x   t-1   dt.

ln(x)

300

What is the definite integral of x(x+2)^3 from 0 to 2

392/5

400

This integral gives the area to the right of x = h(y) and to the left of x = g(y) between y = c and y = d.

∫cd   (g(y)-h(y))   dy

500

This number is the value of the integral ∫-11 (1-x2)1/2.

pi/2

Graph Practice

100

The graph of f is this on an interval where f'(x) is negative.

Decreasing

200

This is a point where the derivative of f either does not exist or equals zero.

Critical Point

300

This sign change of f'(x) guarantees that a critical point c is a local maximum.

Positive to Negative

400

These are the points where an absolute maximum or minimum of a function on a closed interval may occur.

Critical Points and Endpoints

500

This equation gives the horizontal asymptote for the function

f(x) = (3x2+5x+4)/(5x2+x +17).

y = 3/5