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Can someone help me get started on deriving the Maclaurin series?
I'm having trouble finding the Maclaurin series for f(x) = ln(2 + x^2). I'm supposed to derive it using the known M series equations for e^x, sinx, and/or 1/(1 - x), but I have no idea where to get started.
2 Answers
- Awms ALv 71 decade agoFavorite Answer
Try starting with
1 / (2 + x) = (1/2) / (1 - (-x/2) ).
Integrate it, then change the x to an x^2.
- ?Lv 45 years ago
MaClaurin sequence for e^x=one million+x + x^two/two! + x^three/three! ... So e^(2x)= one million+(2x) + (2x)^two/two! + (2x)^three/three! + (2x)^four/four! ... x^two*e^(2x)= x^two + 2x^three + two^two*x^four/two! + two^three*x^five/three! + two^four*x^6/four! ... Remember that f(x)= f(zero) + f'(zero)*x + f''(zero)*x^two/two! + f'''(zero)*x^three/three!... wherein that is the Taylor sequence with a=zero Derive e^x on this type.
