(a) Find the fourth order Taylor polynomial for f(z) = re about z = 0. (b) Using the polynomial from part (a), find a Taylor polynomial expansion about 1= 0 for f te"dt and use it to approximate f, te"dt leaving your final solution correct to 5 decimal places.

Advanced Engineering Mathematics
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ISBN:9780470458365
Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
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Question 1
(a) Find the fourth order Taylor polynomial for f(x) = re about z = 0.
(b) Using the polynomial from part (a), find a Taylor polynomial expansion about
I = 0 for te"dt and use it to approximate te"dt leaving your final solution
correct to 5 decimal places.
Transcribed Image Text:Question 1 (a) Find the fourth order Taylor polynomial for f(x) = re about z = 0. (b) Using the polynomial from part (a), find a Taylor polynomial expansion about I = 0 for te"dt and use it to approximate te"dt leaving your final solution correct to 5 decimal places.
Expert Solution
Step 1

The nth order Taylor polynomial of a function f(x) about x=a is defined by fxP(x)=f(a)+f'(a)1!(x-a)+f''(a)2!(x-a)2+f'''(a)3!(x-a)3+ +f(n)(a)n!(x-a)n.

Then, the fourth-order Taylor polynomial is as follows: P(x)=f(a)+f'(a)1!(x-a)+f''(a)2!(x-a)2+f'''(a)3!(x-a)3+f(4)(a)4!(x-a)4.

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