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40 Cards in this Set
- Front
- Back
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cos^2(x)
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1/2 (1+cos(2x)
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sin^2(x)
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1/2(1-cos(2x)
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derivative of:
sin(x) |
integral of:
cos(x) |
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derivative of:
cos(x) |
integral of:
-sin(x) |
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derivative of:
tan(x) |
integral of:
sec^2(x) |
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derivative of:
csc(x) |
integral of:
-csc(x)cot(x) |
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derivative of:
sec(x) |
integral of:
sec(x)tan(x) |
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derivative of:
cot(x) |
integral of:
-csc^2(x) |
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sin^2(x) + cos^2(x)=?
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1
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tan^2(x)+1=?
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sec^2(x)
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1 + cos^2(x)=?
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csc^2(x)=?
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derivative of:
sin^-1(x) |
integral of
1/sqrt(1-x^2) |
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derivative of:
cos^-1(x) |
integral of
-1/sqrt(1-x^2) |
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derivative of:
tan^-1(x) |
integral of:
1/(1+x^2) |
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derivative of:
a^x |
integral of:
a^x ln(a) |
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derivative of:
e^x |
integral of:
e^x |
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derivative of:
ln(x) |
integral of:
1/x, x>0 |
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derivative of:
loga(x) |
integral of:
1/xln(a) |
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derivative of:
sinh(x) |
integral of:
cosh(x) |
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derivative of:
cosh(x) |
integral of:
sinh(x) |
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derivative of:
tanh(x) |
integral of:
sech^2(x) |
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integral of:
ln(u)du |
uln(u)-u +c
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integral of:
tan(u)du |
ln(abs(sec(u))) +c
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integral of:
sec(u)du |
ln(abs(sec(u)+tan(u))+c
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integral of:
csc^2(u)du |
-cot(u)+c
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integral of:
cot(u)du |
ln(abs(sin(u)) +c
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integral of:
1/sqrt(a^2 - u^2) du |
arcsin(u/a)+c
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integral of:
1/a^2 + u^2 du |
1/a arctan(u/a)+c
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integral of:
1/ u*sqrt(u^2 - a^2) du |
1/a arcsec(u/a)+c
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integration by parts formula
and what do you choose first? |
integral u*dv= uv - [integrand]vdu
choose u and dv |
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sqrt(a^2-b^2 x^2)
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x=a/b sin(theta)
use: cos^2(theta)=1-sin^2(theta) -pi/2 =/< theta =/< pi/2 |
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sqrt(b^2 x^2 -a^2)
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x=a/b sec(theta)
use tan^2(theta)=sec^2(theta)-1 0=/< theta < pi/2 OR pi=/<theta<3pi/2 |
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sqrt(a^2 + b^2 x^2)
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x=a/b tan(theta)
use tan^2(theta)=sec^2(theta)-1 -pi/2 < theta < pi/2 |
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integral of sin^n(x) * cos^m(x) dx
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1. if n is ODD, strip one sine out, convert remaing sins to cosines using trig identity, use u=cos(x)
2. if m is odd, strip one sine out, convert to sines, use u=sin(x) 3. both even then use trig identities |
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integral of tan^n(x) * sec^m(x)
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1. if n is odd, strip one of each, turn into secants, use u=sec(x)
2. if m is even, strip 2 secants and convert to tangents, use u=tan(x) |
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conditions needed for:
integral test |
f(x) must be continuous, positive, and decreasing on the given interval
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conditions needed for:
regular comparison and limit comparison tests |
both the original and the "known" series must have all positive terms on the given interval
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conditions needed for:
alternating series test |
bn must be positive
bn must be decreasing and lim as n->infinity of bn=0 |
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Taylor Series Eqn.
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f(x)= sum from n=0, infinity of f^n (a)*a*[(x-a)^n/n!]
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L'Hospitals rule can be applied when...?
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limit is in indeterminate form aka 0/0 or infinity/infinity
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