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Let f be a function such that f(0) = 3 and the nth derivative of f at x 0 is given by pl0) = -1)** (n +1)! 2" for integer values of n from 1 to 4. a. Write the third-degree Taylor polynomial for f about x 0 and use it to approximate f(-02). b. Write the fourth-degree Taylor polynomial for g about x= 0 where g(x)= /(x?). c. Let h be the function given by h(x) = | f(1) dt. Write the third-degree Taylor polynomial for h about x= 0.

Let f be a function such that f(0) = 3 and the nth derivative of f at x 0 is given by pl0) = -1)** (n +1)! 2" for integer values of n from 1 to 4. a. Write the third-degree Taylor polynomial for f about x 0 and use it to approximate f(-02). b. Write the fourth-degree Taylor polynomial for g about x= 0 where g(x)= /(x?). c. Let h be the function given by h(x) = | f(1) dt. Write the third-degree Taylor polynomial for h about x= 0.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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3 Let f be a function such that /(0) and the nth derivative of f at x=0 is given by pla0) = -1)** (n + 1)! 2" for integer values of n from I to 4. a. Write the third-degree Taylor polynomial for f about x 0 and use it to approximate f(-02). b. Write the fourth-degree Taylor polynomial for g aboutx=0 where g(x)=f(r). c. Let h be the function given by h(x) = | f(1) dt. Write the third-degree Taylor polynomial for h about x= 0. d. Let h be the function defined as in part (c). If f(-1) = 5, find the exact value of h(-1) or explain why it cannot be determined.
Transcribed Image Text:3 Let f be a function such that /(0) and the nth derivative of f at x=0 is given by pla0) = -1)** (n + 1)! 2" for integer values of n from I to 4. a. Write the third-degree Taylor polynomial for f about x 0 and use it to approximate f(-02). b. Write the fourth-degree Taylor polynomial for g aboutx=0 where g(x)=f(r). c. Let h be the function given by h(x) = | f(1) dt. Write the third-degree Taylor polynomial for h about x= 0. d. Let h be the function defined as in part (c). If f(-1) = 5, find the exact value of h(-1) or explain why it cannot be determined.
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