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Asked Dec 3, 2019
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Use the definition of a Taylor series to find the first four nonzero terms of the series for f(x) centered at the given value of a. (Enter your answers as a comma-separated list.)
f(x) 3xe*
a 0
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Use the definition of a Taylor series to find the first four nonzero terms of the series for f(x) centered at the given value of a. (Enter your answers as a comma-separated list.) f(x) 3xe* a 0

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Expert Answer

Step 1

A Taylor series is a series expansion of a function about a point. A Taylor series is an expansion of a real function  f(x) about a point x = a is given by

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S(x)-f(а)+f(а)(х-а) s(а(x-а) +. f"(a) ?(x- а) +. (х—. 2! 3! п!

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Step 2

Here in the given question a = 0:

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xif"(0)xf"(0) x"f (a) +.. f(x) f(0)+f(0)+ 2! +... + 3! n!

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Step 3

For the given function f(x) = 3xex...

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>f(0)= 0 f(0) 3 f(x)= 3xe f'(x) 3xe 3e f'(x) 3xe +3e° +3e* f"(0) 6 f"(x)= 3xe +3e + 3e*+3e° - f"(0)= 9 f(x)= 3xe +3e +3e +3e*+3e f(0)= 12

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