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23 Cards in this Set
- Front
- Back
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How is f(x)=e^x represented as a Maclaurin series? What is the interval of convergence of this series?
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(the sum as n runs from 0 to infinity of) (x^n)/(n!)
Convergent for all values of x |
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How is f(x)=sin(x) represented as a Maclaurin series? What is the interval of convergence of this series?
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(the sum as n runs from 0 to infinity of) ((-1)^n x^(2n+1)) / (2n+1)!
Convergent for all values of x |
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How is f(x)=cos(x) represented as a Maclaurin series? What is the interval of convergence of this series?
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(the sum as n runs from 0 to infinity of) ((-1)^n x^(2n)) / (2n)!
Convergent for all values of x |
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How is f(x)=tan^-1(x) represented as a Maclaurin series? What is the interval of convergence of this series?
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(the sum as n runs from 0 to infinity of) ((-1)^n x^(2n+1)) / (2n+1)
Convergent on interval [-1,1] |
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How is f(x)=1/(1-x) represented as a Maclaurin series? What is the interval of convergence of this series?
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(the sum as n runs from 0 to infinity of) x^n
Convergent on interval (-1,1) |
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How is f(x)=1/(1-x) represented as a power series? What is the interval of convergence?
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(the sum as n runs from 0 to infinity of) x^n
abs. value of x<1 |
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What is the integral of f(x)=sec^2(x) ?
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tan(x)
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What is the integral of f(x)=csc^2(x) ?
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-cot(x)
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What is the integral of f(x)=sec(x)tan(x) ?
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sec(x)
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What is the integral of f(x)=csc(x)cot(x) ?
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-csc(x)
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What is the integral of f(x)=1/(x^2 + 1) ?
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tan^-1(x)
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What is the integral of f(x)=1/(1-x^2)^(1/2)
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sin^-1(x)
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How is (1+x)^k represented as a binomial series?
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(the sum as n runs from 0 to infinity of) (k n) x^n
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What is the coefficient (k n)?
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(k(k-1)(k-2)....(k-n+1))/n!
n=1,2,3........k |
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How is (a+b)^k represented as a binomial series?
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(the sum as n runs from 0 to infinity of) (k n) a^(k-n)b^n
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What is Demoivres theorem?
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z^n=r^n((cos nx)+isin nx))
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What is 1/z?
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1/z=1/r(cos x - isin x)
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What is z^(1/n)?
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z^(1/n)=r^(1/n)(cos x+2kpi/n + isin x+2kpi/n)
k=0, 1, 2.... n-1 |
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In polar form of a complex number, what is r?
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r=the square root of (a^2 + b^2)
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When is a geometric series convergent?
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When absolute value of r<1
ar^n-1 |
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When is a p-series convergent?
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When p>1
1/n^p |
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What do the different results of the ratio test tell you?
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if L<1 convergent
if L>1 divergent if L=1 inconclusive |
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What is the sum of a geometric series?
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S=a/(1-r)
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