BenderMath 21DFinal Exam11:30–2:30 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∞Xn=0(x-2)nn+1.(a) For what values ofxis the series absolutely convergent? Your answer should bean interval forx; that is, an expression likea≤x<b,ora<x<b, etc.(b) For what values ofxis the series conditionally convergent?2. (60 pts) Solve the following diﬀerential equations. If initial conditions are given, ﬁndthe particular solution. If there are no initial conditions, ﬁnd the general solution.(a)y0=2x-yx;y(0) = 2.(b)x2y00+3xy0-3y=0;y(1) = 4,y0(1) = 0.(c)y00-4y=16lnt.You may leave integrals in your answer to (c).3. (20 pts) Consider the diﬀerential equation
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