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27 Cards in this Set
- Front
- Back
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[TI, sin(x)^m*cos(x)^n] When m is odd... |
u = cos(x) |
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[TI, sin(x)^m*cos(x)^n] When n is odd... |
u = sin(x) |
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[TI, sin(x)^m*cos(x)^n] When m and n are odd... |
Either u = sin(x) or u = cos(x) |
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[TI, sin(x)^m*cos(x)^n] When m and n are even... |
Use half-angle formulas to simplify |
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[TI, sec(x)^m*tan(x)^n] When m is even... |
u = tan(x) |
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[TI, sec(x)^m*tan(x)^n] When n is odd... |
u = sec(x) |
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[TI, sec(x)^m*tan(x)^n] When m is even or n is odd... |
Either u = tan(x) or u = sec(x) |
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[TI, sec(x)^m*tan(x)^n] When m is odd or n is even... |
No guidelines; try simplifying to sec(x) or sec(x)^3 |
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[TS] sqrt(a^2 - x^2) |
x = a*sin(u) |
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[TS] sqrt(a^2 + x^2) or 1/(a^2 + x^2) |
x = a*tan(u) |
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[TS] sqrt(x^2 - a^2) |
x = a*sec(x) |
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How to tell if a series is increasing or decreasing |
(a_(n+1))/(a_n), (a_(n+1)) - (a_n), (a_n)' |
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(a_(n+1))/(a_n) |
If answer is 1 + (smth) --> increasing |
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(a_(n+1)) - (a_n) |
If answer is positive --> increasing |
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(a_n)' |
If answer is positive --> increasing |
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Geometric series convergence |
abs(r) < 1 --> converge to a/(1-r) abs(r) > 1 --> diverge |
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nth term test: result |
If lim(a_n) to inf doesn't equal 0, it diverges |
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Integral test: requirements |
Positive, continuous, decreasing on [1,inf) |
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Integral test: results |
If limit of integral of a_n is a number --> converge If DNE or infinity --> diverge |
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Limit comparison test: requirements |
Positive terms |
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Limit comparison test: results (for a_n) |
If lim(a_n/b_n) to infinity is a POSITIVE FINITE NUMBER --> a_n has same behavior as b_n Else --> inconclusive If L = 0 and b_n converges, a_n does too |
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Alternate series test: results (for (-1)^n*a_n) |
If a_n is decreasing and lim(a_n) to infinity is 0 --> converges |
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Ratio test: performance |
lim(abs(a_(n+1)/a_n)) to infinity |
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Root test: performance |
lim((abs(a_n))^(1/n)) to infinity |
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Ratio and root test: results |
If L < 1: converge If L > 1 of L = inf : diverge If L = 1 : inconclusive |
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Power series: performance |
1. Find c 2. Conduct ratio test 3. L from ratio test determines where is converges 4. Endpoint - c = R |
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p-series: results |
p > 1: converge 0<p<=1: diverge |
