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CTK Exchange
Angkasa
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May-24-07, 08:15 AM (EST) |
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"Taylor's math"
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given that f(x)= (1+x)ln (1+x), A)find the fifth derivative of f(x) B)find that the first five non-zero terms in the Taylor expansion. camana mo solve |
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JJ
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May-26-07, 08:40 AM (EST) |
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1. "RE: Taylor's math"
In response to message #0
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f(x)= (1+x)ln(1+x) first derivative : 1+ln(1+x) second : 1/(1+x) third : -1/(1+x)^2 fourth : 2/(1+x)^3 fifth : -6/(1+x)^4 etc. n-th. : ((-1)^(n-1))((n-2)!)/(1+x)^(n-1) Taylor expansion: f(x) = x +(1/2)(x^2) -(1/6)(x^3) +(1/12)(x^4) +...+ ((-1)^n)(1/(n-1))(1/n)(x^n) +... |
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