AP Calculus AB Review (BRHS)

Derivatives

100

d/dx(3x^2+4x-7)

6x+4

200

d/dx(cosx)

-sinx

300

d/dx(xe^(2x))

e^(2x)+2x*e^(2x)

400

d/dx(arctan(3x))

3/(1+9x^2)

500

d/dx(x^2/(ln(x)))

(2x*ln(x)-x)/(ln(x))^2

Formulas

100

sin^2x+cos^2x=

1

200

f'(g(x))g'(x)

What is the chain rule?

300

(g(x)f'(x)-f(x)g'(x))/(g(x))^2

What is quotient rule?

400

f'(x)g(x)+f(x)g'(x)

What is product rule?

500

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

What is the MVT?

Integrals

100

intdx

x+C

200

inte^(2x)dx

e^(2x)/2+C

300

int(1/(1-2x))dx

-1/2*lnabs(1-2x)+C

400

intsec^2(x/3))dx

3tan(x/3)+C

500

inttanxdx

-lnabs(cosx)+C

Miscellaneous

100

When do you add +C?

When you evaluate an indefinite integral.

200

pi*int((radius_2))^2-(radius_1)^2)dx

What is the washer method?

300

lim_(x->a)f(x) = f(a)

What is the definition of continuity?

400

sin(pi/4)+cos(pi/3)

(1+sqrt2)/2

500

dP/dt = kP(M-P)

What is logistic growth?

Limits

100

lim_(x->oo)1/x

What is 0?

200

lim_(x->0)(cosx-1)/x

What is 0?

300

lim_(x->0)sinx/x

What is 1?

400

lim_(x->0)(3x^2-sinx)/(2x^2+x)

What is -1?

500

lim_(h->0)((3+h)^2-9)/h

f'(3)=6