Stuff You Need to Know Cold - Calculus BC

lim x->0 sinx/x : 1

lim x->0 (1-cosx)/x : 0

Global Max : critical point and f'(x) goes + to -

Points of Inflection : f"(x) = 0 or undefinedf"(x) switches signs

Quotient Rule :

Proving Theorems : ConditionsAnalyzeTheorem

d/dx cot u : -csc^2 u du

d/dx sec u : sec u tan u du

d/dx tan^-1 u : 1/(1+u^2) du

d/dx sec^-1 u : 1/u√u^2-1 du

Mean Value Theorem : instantaneous rate of change = avg rate of change if f(x) is:cont [a,b]diff (a,b)then: f'(c) = f(b)-f(a)/b-a

Rolle's Theorem : if f(x) is:cont [a,b]diff (a,b)f(a) = f(b)then: f'(c) = 0

Washer Method : V(x) = pi∫a->b (R(x))^2-(r(x)^2

General Volume Equation : V(x) = ∫a->b A(x)dx