21d_99f_fe

# 21d_99f_fe - Bender Math 21D Final Exam 11:302:30 Thursday...

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

Bender Math 21D Final Exam 11:30–2:30 Thursday 12/16/99 Please put your name, ID number, and section number (or time) on your blue book. The ﬁrst page of your blue book may contain notes. No other paper is allowed. Calculators are NOT allowed. You must show your work to receive credit. 1. (20 pts) Consider the series X n =0 ( x - 2) n n +1 . (a) For what values of x is the series absolutely convergent? Your answer should be an interval for x ; that is, an expression like a x<b ,or a<x<b , etc. (b) For what values of x is the series conditionally convergent? 2. (60 pts) Solve the following diﬀerential equations. If initial conditions are given, ﬁnd the particular solution. If there are no initial conditions, ﬁnd the general solution. (a) y 0 = 2 x - y x ; y (0) = 2. (b) x 2 y 00 +3 xy 0 - 3 y =0; y (1) = 4, y 0 (1) = 0. (c) y 00 - 4 y =16ln t . You may leave integrals in your answer to (c). 3. (20 pts) Consider the diﬀerential equation
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

Ask a homework question - tutors are online