AP Calculus Midterm Study Guide

limit

limit

• the tendency of a function

• expected “y” value for a given “x” value

derivative

• the slope of the tangent line

• the instantaneous rate of change

tangent line

touches a curve only at one point & matches the slope of the curve of that point

secant line

line that intersects the curve at 2 points

average rate of change formula

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

instantaneous velocity formula

s’(t) = v(t)

average acceleration

v(t₂) - v(t₁ ) / t₂ - t₁

instantaneous acceleration

s’’(t) = v’(t) = a(t)

power rule

y’ = n * x^n-1

product rule

y’ = f(x)g’(x) + f’(x)g(x)

quotient rule

g(x)f’(x) - f(x)g’(x) / [g(x)]²

chain rule

y’ = f’(g(x))g’(x)

y = sinx

cosx

y = cosx

-sinx

y = tanx

sec^2x

y = cscx

-cscxcotx

y = sec x

secxtanx

y = cotx

-csc^2x

explicit equation

y = x²+5 (variable by itself)

implicit equation

x² + y² = 25 (two different variables)

1/sin

csc

1/cos

sec

1/tan

cot