2414 HW 20 Taylor Series1

pdf

School

Texas A&M University *

*We aren’t endorsed by this school

Course

151/152

Subject

Mathematics

Date

Apr 3, 2024

Type

pdf

Pages

Uploaded by DeanReindeer4728

Calculus 2 (2414) Name: Unit 4: Taylor Series and Polar Coordinates Homework 20: Taylor Series Please make sure your solutions are easily legible and that they clearly communicate the methods you used to arrive at your final answer. You are welcome to use a calculator or online calculation engine on your homework, but be prepared to make basic calculations by hand on exams. 1. For f ( x ) = e x , determine its Taylor series centered at 0 (also called its Maclaurin series) and the corresponding interval of convergence.

Calculus 2 Homework 20 Page 2 of ?? 2. For f ( x ) = cos x , determine its Taylor series centered at 0 (also called its Maclaurin series) and the corresponding interval of convergence.

Calculus 2 Homework 20 Page 3 of ?? 3. For f ( x ) = 1 1 − x , determine its Taylor series centered at 0 (also called its Maclaurin series) and the corresponding interval of convergence.

Your preview ends here

Eager to read complete document? Join bartleby learn and gain access to the full version

Access to all documents
Unlimited textbook solutions
24/7 expert homework help

Calculus 2 Homework 20 Page 4 of ?? 4. For f ( x ) = 1 1 − x , determine its Taylor series centered at 3 and the corresponding interval of convergence.

Calculus 2 Homework 20 Page 5 of ?? 5. For f ( x ) = tan − 1 x , determine its Taylor series centered at 0 (also called its Maclaurin series) and the corresponding interval of convergence.

Calculus 2 Homework 20 Page 6 of ?? 6. Considering the fact that the Maclaurin series representation of f ( x ) = tan − 1 x is an alternating series, determine how many terms of the series you need to approximate π 4 with an error less than 0 . 001.

Your preview ends here

Eager to read complete document? Join bartleby learn and gain access to the full version

Access to all documents
Unlimited textbook solutions
24/7 expert homework help

Calculus 2 Homework 20 Page 7 of ?? 7. Substitute − x 2 for x in the Maclaurin series of e x to find the Maclaurin series for e − x 2 . Use this new series to approximate Z 1 0 e − x 2 dx with an error less than 0 . 01.

2414 HW 20 Taylor Series1

Related Documents