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Q. 9

Found in: Page 692


Book edition 1st
Author(s) Peter Kohn, Laura Taalman
Pages 1155 pages
ISBN 9781429241861

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Short Answer

If f(x)=4x3-5x2+6x+1 and P3(x) is the third Taylor polynomial for f at −1, what is the third remainder R3(x)? What is R4(x)? (Hint: You can answer this question without finding any derivatives.)

The required values are R3(x)=0 and R4(x)=0

See the step by step solution

Step by Step Solution

Step 1. Given Information 

The given function is f(x)=4x3-5x2+6x+1

Step 2. Calculation

The formula to calculate the remainder is Rn(x)=fn+1(c)(n+1)!(x-x0)n+1

Substitute n as 3 to find the third remainder of the function.


Since the given degree has highest degree 3 which implies that f4(c)=0

Hence, R3(x)=0


localid="1649315178808" R4(x)=f4+1(c)(4+1)!(x-x0)4+1=f5(c)5!(x-x0)5 =05!(x-x0)5=0

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