AP Calculus BC - Stuff You Must Know

L'Hôpital's Rule

Slope of a Parametric equation

Euler’s Method

Polar Area

Polar Slope

Integration by parts

Integral of logarithms

Ratio Test

sin(2x)

2sin(x)cos(x)

cos(2x)

cos^2(x) - sin^2(x)

cos(2x)

1 - 2sin^2(x)

cos^2(x)

1/2(1+cos(2x))

sin^2(x)

1/2(1-cos(2x))

sin^2(x) + cos^2(x)

1

1+tan^2(x)

sec^2(x)

cot^2(x) + 1

csc^2(x)

sin(-x)

-sin(x)

cos(-x)

cos(x)

Taylor Series

f(x) = f(a) + f’(a)(x-a) + [f’’(a)(x-a)^2 / 2!] + [f’’’(a)(x-a)^3 / 3!] + …

Lagrange Error Bound

Maclaurin Series

Alternating Series Error Bound

Geometric Series

sin(0)

0

cos(0)

1

tan(0)

0

sin(pi/6)

1/2

cos(pi/6)

root3/2

sin(pi/4)

root2/2

cos(pi/4)

root2/2

sin(pi/3)

root3/2

cos(pi/3)

1/2

sin(pi/2)

1

cos(pi/2)

0

Chain Rule

Product Rule

Quotient Rule

Trapezoidal Rule

NEVER FORGET (for integrals)

+C

Average Value

d/dx sin(x)

cos(x)

d/dx cos(x)

-sin(x)

d/dx tan(x)

sec^2(x)

d/dx cot(x)

-csc^2(x)

d/dx sec(x)

sec(x)tan(x)

d/dx csc(x)

-csc(x)cot(x)

d/dx ln(u)

1/u

Solid Disk Method

Solid Washer Method

Cartesian Arc Length

Polar Arc Length

Parametric Arc Length

Intermediate Value Theorem

If the function f(x) is continuous on [a,b], then f(x) achieves every value between f(a) and f(b) in the open interval (a,b).

Mean Value Theorem

If the function f(x) continuous on [a,b], and the first derivative exists on the interval (a,b), then there is at least one number x = c in (a,b) such that f’(c) = [ f(b)-f(a) ] / (b-a).

Rolle’s Theorem

Same as mean value theorem but if f(a) = f(b), then there is at least one number x = c in (a,b) such that f’(c) = 0.

d/dx loga(x)

1/xln(a)

Displacement

Speed

Distance