{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

GoodmanW98T4

# GoodmanW98T4 - 8 ≤ x ≤ 1 2 5[10 points Find the Taylor...

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

Math 21H Apr. 21, 1998 Test #4 Name: Read each question carefully, and be sure to show clearly how you got your answers as well as what your answers are. 1. [10 points] Find a function f ( x ) such that f 0 ( x ) = ( xf ( x )) 2 and f (1) = - 3. 2. [10 points] Find the area of the surface obtained by rotating the curve y = x 2 , for 0 x 1, around the y -axis. 3. [10 points] Find the Maclaurin series for the function f ( x ) = 1 1 + 3 x and determine its interval of convergence. 4. [15 points] (a) Approximate f ( x ) = 1 /x by a Taylor polynomial with degree n = 3 centered at a = 1; and (b) use Taylor’s formula to estimate the accuracy of this approximation for
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: . 8 ≤ x ≤ 1 . 2. 5. [10 points] Find the Taylor series centered at a = 2 for the function f ( x ) = e x . 6. [15 points] Use a power series to approximate Z . 5 1 √ 1 + x 3 dx accurate to four decimal places. 7. [10 points] Write an integral for the length of the curve y = cos x with 0 ≤ x ≤ π , but do not evaluate the integral. 8. [10 points] Find the centroid of the region bounded by y = e x , y = 0, x = 0, and x = 1. 9. [10 points] If f ( x ) = e 2 x cos x , use power series to ﬁnd f (4) (0)....
View Full Document

{[ snackBarMessage ]}

Ask a homework question - tutors are online