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AP Calculus Formula Quiz

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Section 1

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d/dx (arctan x) =

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Calculus Math

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Mar 1, 2020

Cards (36)

Section 1

(36 cards)

d/dx (arctan x) =

Front

Back

Speed is increasing if

Front

acceleration and velocity are both positive or both negative.

Back

d/dx(csc x) =

Front

Back

The integral from a to b of q'(t)dt is

Front

q(b) - q(a)

Back

d/dx (cot x) =

Front

Back

Average value from a to b of f is

Front

1/(b-a) (the integral from a to b of f)

Back

d/dx (arcsin x) =

Front

Back

A function w has a point of inflection at x=c if w'

Front

changes directions at x=c.

Back

If the lim (x->3) (g(x)) exists, then lim(x->3+)(g(x)) =

Front

lim(x->3-)(g(x))

Back

The integral from a to b of q''(t) dt is

Front

q'(b) - q'(a)

Back

d/dx (f(g(x))) =

Front

Back

Write the limit definition of a derivative.

Front

Back

d/dx (-cos x) =

Front

sin x

Back

A function f has a relative min at x=c if f'

Front

changes from negative to positive at x=c

Back

A function w has a point of inflection at x=c if w''

Front

changes signs at x=c.

Back

The formula for the tangent line at x=a is

Front

y-f(a) = f'(a)(x-a)

Back

A function f has a relative max at x=c if f''

Front

is negative at x=c AND f'=0 at x=c

Back

The formula for total distance traveled by an object from t=a to t=b is

Front

The integral from a to b of |v(t)|dt

Back

A function w has a point of inflection at x=c if w

Front

changes concavity at x=c.

Back

A function f has a relative min at x=c if f''

Front

is positive at x=c AND f'=0 at x=c

Back

The integral from a to b of q(t)dt is

Front

Q(b) - Q(a)

Back

d/dx(tan x) =

Front

Back

A function f has a relative max at x=c if f'

Front

changes from positive to negative at x=c

Back

The integral of cos x =

Front

sin x + C

Back

d/dx(sec x)

Front

Back

d/dx (the integral from a to x of q(t)dt) is

Front

q(x)

Back

State the Mean Value Theorem for Integrals.

Front

Back

Average rate of change of f from a to b given f'(x) is

Front

1/(b-a) (the integral from a to b of f'(x))

Back

Speed is decreasing if

Front

acceleration and velocity have opposite signs.

Back

d/dx (f(x)/g(x)) =

Front

Back

The formula for displacement of an object from t=a to t=b is

Front

The integral from a to b of v(t)dt

Back

State the Mean Value Theorem for Derivatives.

Front

Back

Average rate of change from a to b of f is

Front

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

Back

d/dx (f(x)g(x)) =

Front

Back

d/dx (arccos x) =

Front

Back

If g is continuous at x=3 then according to the definition of continuity, lim(x->3+)(g(x))=

Front

lim(x->3-)(g(x)) = g(3)

Back