AP Calculus AB

Limits

100

Evaluate lim x->2 (x²-4)/(x-2)

4

200

Find the vertical asymptote of f(x)=1/(x-3)

3

300

Evaluate lim x->infinity (3x²+1)/(x²-5)

3

400

Explain continuity at a point

A function that has no sudden breaks, jumps, or holes at a specific location

500

Evaluate lim x->0 sin(x)/x

1

Derivatives

100

Find d/dx of x³+4x

3x²+4

200

Find d/dx of sin(x) 

cos(x)

300

Find d/dx of ln(x)

1/x

400

Differentiate y=x²e^x

y'=2xe^x+x²e^x

500

Use implicit differentiation x²+y²=25

-x/y

Integrals

100

x²dx

x³/3 +C

200

cos(x)dx

sin(x)+C

300

Evaluate int(0,1)xdx

1/2

400

What's the meaning of the area under a curve?

Accumulated change represented by the definite integral

500

Find average value of int (0,4) 2x²+4x-7

35/3 or 11.67

FTC

100

FTC part 1

The integral on (a, b) of f(x) dx = F(b) - F(a)

200

FTC part 2

If f is continuous on an open interval containing a, then for every x in the interval the derivative of the the integral of f(x) dx on said interval is equal to f(x)

300

d/dx int (0,x) t²dt

x²

400

Evaluate int (1,3) 2xdx

8

500

What's the connection between derivatives and integrals?

They are inverse

Theorems

100

Intermediate Value Theorem

If f is continuous on the closed interval [a,b] and k is any number between f(a) and f(b) then there is at least one number c in [a, b] such that f(c) = k

200

Product Rule

d/dx (f(x) g(x)) = f(x)g'(x) + g(x) f'(x)

300

Quotient Rule

d/dx (g(x)/ h(x)) = (h(x) g'(x) - g(x) h'(x))/ h(x)^2

400

Mean Value Theorem

f'(c) = (f(b) - f(a))/ (b - a)

500

Average Value Theorem

1/ (b-a) times the integral on (a, b) of f(x) dx