f(x) = E(-1)" Vn(x – 4)" n! n=0 what is f(7) (4)?

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter5: Inverse, Exponential, And Logarithmic Functions
Section: Chapter Questions
Problem 18T
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Question
f(x) = E(-1)" Vn(x – 4)"
n!
n=0
what is f(7) (4)?
Transcribed Image Text:f(x) = E(-1)" Vn(x – 4)" n! n=0 what is f(7) (4)?
Expert Solution
Step 1

In the seventh derivative of f(x) at x = 4, the only term contributing meaningfully will be the term corresponding to n = 7. All the earlier terms will get lost during differentiation. All the later terms will get lost as they will still contain some power of (x - 4) after differentiation 7 times, which will eventually become 0 on substituting x = 4.

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