Question

25. Let \( g(x)=p(x)+x^{n+1} f(x) \), where \( p(x) \) is a polynomial of degree at most \( n \) and \( f \) has derivatives through order \( n \). Show that \( p(x) \) is the Maclaurin polynomial of order \( n \) for \( g \).

Name: 25. Let g(x)=p(x)+x^n+1 f(x), where p(x) is a polynomial of degree at most n and f has derivatives through order n. Show that p(x) is the Maclaurin polynomial of order n for g.
Uploaded: 2021-05-06T14:41:33-08:00
Duration: 2 min 35 s
Channel: Suzanne W.
Description: 25. Let g(x)=p(x)+x^n+1 f(x), where p(x) is a polynomial of degree at most n and f has derivatives through order n. Show that p(x) is the Maclaurin polynomial of order n for g.

          25. Let \( g(x)=p(x)+x^{n+1} f(x) \), where \( p(x) \) is a polynomial of degree at most \( n \) and \( f \) has derivatives through order \( n \). Show that \( p(x) \) is the Maclaurin polynomial of order \( n \) for \( g \).

25. Let g(x)=p(x)+x^n+1 f(x), where p(x) is a polynomial of degree at most n and f has derivatives through order n. Show that p(x) is the Maclaurin polynomial of order n for g.

Added by Darnell C.

Calculus of a Single Variable

Ron Larson, Bruce Edwards 10th Edition

Chapter 9

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25. Let \( g(x)=p(x)+x^{n+1} f(x) \), where \( p(x) \) is a polynomial of degree at most \( n \) and \( f \) has derivatives through order \( n \). Show that \( p(x) \) is the Maclaurin polynomial of order \( n \) for \( g \).