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AP Calculus AB Review

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49 cards

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Section 1

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Calculus Math

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Date created

Mar 1, 2020

Cards (49)

Section 1

(49 cards)

∫cscxcotx

Front

-cscx+C

Back

a(t)<0

Front

v(t) decreasing

Back

v(t)>0

Front

p(t) is moving right

Back

d/dx(tan⁻¹u)

Front

u'/(1+u²)

Back

∫cosx dx

Front

sinx+C

Back

∫csc²x dx

Front

-cotx+C

Back

d/dx(sin⁻¹u)

Front

u'/√(1-u²)

Back

a(t)>0

Front

v(t) increasing

Back

∫sinx dx

Front

-cosx+C

Back

Chain rule of f(x)^n

Front

nf(x)f'(x)

Back

d/dx(cotx)

Front

-csc²x

Back

Alternate Definition of Derivative

Front

limit (as x approaches a number c)= f(x)-f(c)/(x-c), x≠c

Back

Limit Definition of Derivative

Front

limit (as h approaches 0)= {f(x+h)-f(x)}/h

Back

average value

Front

(1/(b-a))[∫f(x)dx] [BOUNDED BY A TO B]

Back

∫du/(a²+u²)

Front

(1/a)(tan⁻¹u/a)+C

Back

d/dx(sinx)

Front

cosx

Back

∫du/√(a²-u²)

Front

(sin⁻¹u/a)+C

Back

Displacement of particle

Front

∫v(t)dt

Back

total distance of particle

Front

∫|v(t)|dt

Back

Intermediate Value Theorem

Front

if f(x) is continuous on [a,b], then there will be a point x=c that lies in between [a,b]

Back

∫k dx [k IS A CONSTANT]

Front

kx+C

Back

d/dx(tanx)

Front

sec²x

Back

If f'(x)<0

Front

f(x) is decreasing

Back

∫(x^n)dx

Front

x^(n+1)∕(n+1) +C

Back

d/dx(secx)

Front

secxtanx

Back

p'(t)

Front

v(t)= velocity

Back

Area between curves

Front

A=∫f(x)-g(x) dx

Back

If f'(x)>0

Front

f(x) is increasing

Back

d/dx(cosx)

Front

-sinx

Back

v(t) and a(t) has different signs

Front

speed of particle decreasing

Back

∫secxtanx dx

Front

secx+C

Back

d/dx(cscx)

Front

-cscxcotx

Back

Product rule of f(x)g(x)

Front

f'(x)g(x)+g'(x)f(x)

Back

p''(t) or v'(t)

Front

a(t)= acceleration

Back

Power Rule

Front

f(x^n)= nX^(n-1)

Back

Volume (DISK)

Front

V=π∫f(x)²dx

Back

Mean Value Theorem

Front

if f(x) is continuous on [a,b] and differentiable on (a,b), there is at least one point (x=c) where f'(c)= [f(b)-f(a)]/(b-a)

Back

limit as x approaches 0: sinx/x

Front

1

Back

Quotient rule of f(x)/g(x)

Front

[g(x)f'(x)-f(x)g'(x)]/[g(x)]²

Back

d/dx(e^u)

Front

e^u(u')

Back

d/dx(a^u)

Front

a^u(lna)(u')

Back

d/dx(lnu)

Front

u'/u

Back

v(t)<0

Front

p(t) is moving left

Back

∫f(x)dx [BOUNDS ARE SAME]

Front

0

Back

∫(e^kx)dx

Front

ekx/k +C

Back

position of particle at specific point

Front

p(x)= initial condition + ∫v(t)dt (bounds are initial condition and p(x))

Back

∫(1/x)dx

Front

ln|x|+C

Back

v(t) and a(t) has same signs

Front

speed of particle increasing

Back

∫sec²x dx

Front

tanx+C

Back