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Maclaurin expansions

I am struggling to see how the expansion of e^sinx is 1 +x +x/2! -(3x^4)/4! -(8x^5)/5! I know you have to substitute the expansion of sinx into the expansion of e^x but sure the series expansion of sinx is infinite? How does it simplify to finite terms?
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davros
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Original post by Europa192
I am struggling to see how the expansion of e^sinx is 1 +x +x/2! -(3x^4)/4! -(8x^5)/5! I know you have to substitute the expansion of sinx into the expansion of e^x but sure the series expansion of sinx is infinite? How does it simplify to finite terms?


It doesn't - what you have been given must have been the first few terms of the series :smile:

You don't have to substitute one series inside another - sometimes it's helpful, but not always.

I would start from the fundamental definition of the maclaurin series:

f(x) = f(0) + xf'(0) + (x^2)f''(0)/2 + ...

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