Question

If the Maclaurin series of a function f(x) is ?_{n=1}^{?} (-1)? (x? / (3?(n+6))) then f???(0) is equal to 10/3 9/7 8/5 -8/11 -5/13

Name: If the Maclaurin series of a function f(x) is ?n=1^? (-1)? (x? / (3?(n+6))) then f???(0) is equal to 10/3 9/7 8/5 -8/11 -5/13
Uploaded: 2023-09-05T09:52:08-08:00
Duration: 2 min 37 s
Channel: Adi S
Description: If the Maclaurin series of a function f(x) is ?n=1^? (-1)? (x? / (3?(n+6))) then f???(0) is equal to 10/3 9/7 8/5 -8/11 -5/13

          If the Maclaurin series of a function f(x) is ?_{n=1}^{?} (-1)? (x? / (3?(n+6))) then f???(0) is equal to 10/3 9/7 8/5 -8/11 -5/13

Added by William T.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Adi S

09/05/2023

Step 1

To do this, we need to find the coefficient of the x^5 term in the series for f(x). Let's divide the series for 19f(x) by 19: $$f(x) = \sum_{n=1}^{\infty} \frac{(-1)^n 3^n (n+6)}{19} x^{n-1}$$ Now, we want to find the coefficient of the x^5 term in the series Show more…

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