MAT 302 Assignment Problem 9.10

MAT 302  Assignment Problem 9.10 | Borough of Manhattan Community College

9.10 Taylor and Maclaurin Series

Question 1

(1 point) Match each of the Maclaurin series with the function it represents.

Question 2

(1 point) Match each of the Maclaurin series with correct function.

Question 3

(1 point) Find the first five non-zero terms of Taylor series centered at x=10x=10 for the function below.

f(x)=lnx

Question 4

(1 point) Find the first five non-zero terms of Maclaurin series (Taylor series centered at x=0x=0) for the function below.

f(x)=x3ex

Question 5

1 point) Find the first five non-zero terms of Maclaurin series (Taylor series centered at x=0x=0) for the function below.

f(x)=sin2x

Question 6

(1 point) Find the first five non-zero terms of Taylor series centered at x=4x=4 for the function below.

f(x)=ex

.

Question 7

 (1 point) Write the Taylor series for f(x)

Find the first five coefficients.

Question 8

(1 point) The function f(x)=ln(10−x)f(x)=ln⁡(10−x) is represented as a power series

Find the first few coefficients in the power series.

Question 9

(1 point) Find the sum of the following series. If it is divergent, type "Diverges" or "D".

Question 10

(1 point)

Write out the first four terms of the Maclaurin series of f(x)f(x) if

f(0)=−12,f′(0)=11,f′′(0)=9,f′′′(0)=8

Question 11

(1 point)

Find the Taylor series, centered at c=3c=3, for the function

f(x)=1x.

Question 12

(1 point)

Find the Maclaurin series and corresponding interval of convergence of the following function.