RandolphT4aW98

RandolphT4aW98 - Explain how you know that your answer is...

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
Winter 1998 Math 21 Test #4a (50 pts) Name Show all your work in answering each question. 1. (7 pts) Find the interval and radius of convergence for X n =1 ( - 1) n ( x - 1) n n . 2. (7 pts) Find the Maclaurin series for f ( x )= 1 4 x 2 +1 , and find the interval of convergence for this series. (Hint: use what you know about geometric series.) Interval = 3. (18 pts) (a) Find the Maclaurin series for the function cos( x 2 ). Recall that cos( x )= X n =0 ( - 1) n x 2 n (2 n )! , for all x . (b) Write out T 4 ( x ), the Taylor polynomial of degree 4, for cos( x 2 ). (c) Using your work above, approximate the value Z 0 . 5 0 cos( x 2 ) dx to within .01 of the actual value.
Background image of page 1
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: Explain how you know that your answer is within .01 of R . 5 cos( x 2 ) dx . 4. (18 pts) (a) Find T 2 ( x ), the Taylor polynomial of degree 2, centered at a = 1 for f ( x ) = √ x . (b) Use the expression for the “remainder”, R n ( x ), in Taylor’s Theroem to estimate the error between T 2 (1 . 5) an √ 1 . 5. (c) Use R n ( x ) to estimate the largest possible error if you use T 2 ( x ) to estimate f ( x ) = √ x on the interval [ . 5 , 1 . 5]....
View Full Document

This note was uploaded on 01/24/2011 for the course MATH 21 taught by Professor Mathdep during the Winter '98 term at Missouri S&T.

Ask a homework question - tutors are online