Use the following information to complete parts a. and b. below. 5x f(x) = sin x, a= 3 a. Find the first three nonzero terms of the Taylor series for the given function centered at a. The first nonzero term of the series is

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A: Given: The function f(x)=e-5x.

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Q: f(r) = v2 – a

A: See solution below.

Q: Q7. Find the 1" three terms in Taylor series for f(x) = sinnx near x-0.5.

A: Here we have to find  The 1st three terms in Taylor series for f(x)=sinπx near x=0.5.

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A: Our guidelines we are supposed to answer only one question(because all part are different…

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A: Let's find.

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A: Explanation of the answer is as follows

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A: Let's find.

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A: According to the question we need to find out the McLaurin series.

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Q: Q7. Find the 1" three terms in Taylor series for f(x) = sinnx near x=0.5.

A: Given, f(x)=sinπx

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A: The taylor series of f(x) is given by

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A: Number 15 is only asked.

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A: To identify the function represented by the following power series.∑k=1∞ -1kkxk+24k

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A: We will solve this by Taylor series formula

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A: We can solve this using Taylor series formula

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Q: Find the Taylor Series of the following functions at the given value of a. sin(x) at a = r/4

A: Taylor series about x=a

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Q: For the next two exercises, determine the Maclaurin series for the given function. 2 sin(2/2) 3 2

A: You have asked question no. 2. 2. According to question,Given Function,sinx2

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Q: e substitution to find the Taylor series at

A: By substitution to find the Taylor series at x=0

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Q: 2. f(x) = e2x; a=0, n=10

A: Given:       fx=e2x. a=0, n=10