AP Calc BC Review

Riemann Sums

Euler’s Method

Limit Form of a Derivative (gives equation)

Limit Form of a Derivative at a specific value (gives specific value)

Trapezoidal Sum

Derivatives of Inverse Functions

Integration by Parts

Antiderivative

Function whose derivative = given function (aka, the parent function)

Fundamental Theorem of Calculus

2nd Fundamental Theorem of Calculus

Average Value of a Function

Power Series of Elementary Functions (6)

Intermediate Value Theorem

Mean Value Theorem (Derivatives)

Mean Value Theorem (Integrals)

Extreme Value Theorem

Special Trig Limits (2)

Special Definite Integrals (2)

Why are Absolute Value Functions not differentiable? (explain using limits and the definition of a derivative)

Velocity Vector

Acceleration Vector

Speed

Magnitude of Velocity

Direction

Displacement

Distance Travelled

First Derivative Test

f(x) has relative max/min at x = c where f’(x) changes from ± → ∓ at x= c

Second Derivative Test

f(x) has a relative max/min at x = c where f’(x) = 0 and f’’(x) < or > 0

Volume of any solid

First derivative of a parametric curve given parametric equations x=f(t) and y=g(t)

Second derivative of a parametric curve given parametric equations x=f(t) and y=g(t)

Logistic differential equation

Then, find maximum carrying capacity and where the population is growing fastest

How to test for continuity at a point

Arc Length

dy/dx of a polar curve

(dy/dθ)/(dx/dθ)

x in terms of r

rcosθ

y in terms of r

rsinθ