AP Calc BC formula quiz

definition of e

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definition of absolute value

definition of the derivative

alternative definition of the derivative

definition of continuity

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average rate of change of f(x) on \[a,b\]

intermediate value theorem

if *f* is continuous on \[*a*,*b*\] and *k* is any number between *f(a)* and *f(b*), then there is at least one number *c* between *a* and *b* such that *f(c) = k*

what does d/dx \[c\] equal?

= 0

derivative product rule

d/dx \[*f(x)g(x)*\] = *f’(x)g(x)* + *f(x)g’(x)*

chain rule

d/dx (*f(g(x)*)) = *f’(g(x))* \* *g’(x)*

power rule

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quotient rule

d/dx \[sin *u*\]

= cos *u* du/dx

d/dx \[cos *u*\]

= - sin *u* du/dx

d/dx \[tan *u*\]

= sec^2(*u*) du/dx

d/dx \[sec *u*\]

= sec *u* tan *u* du/dx

d/dx \[csc *u*\]

= -csc *u* cot *u* du/dx

d/dx \[cot *u*\]

= - csc^2 (*u*) du/dx

Rolle’s Theorem

Mean Value Theorem (MVT)

definition of a critical number

definition of increasing functions

definition of decreasing functions

Test for Increasing and Decreasing functions

First Derivative Test

Second Derivative Test

definition of definite integral

integral of …

∫cos u du

sin u + c

∫sin u du

-cos u + c

∫sec²u du

tan u + c

∫sec u tan u du

sec u + c

∫csc²u du

-cot u + c

∫csc u cot u du

-csc u + c

first fundamental theorem of calculus

second fundamental theorem of calculus

integral chain rule

average value of f(x) on [a,b]

derivative of inverse function d/dx [(f^-1)(u)]

d/dx [ln u]

ln |u| + C

∫tan u du/dx

-ln |cos u| + C

∫sec u du/dx

ln |sec u tan u| + C

∫cot u du/dx

ln |sin u| + C

∫csc u du/dx

-ln |csc u + cot u| + C