02spex2 - x 13 in the Taylor-Maclaurin series of f ( x ) =...

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MATH 222 — SECOND MIDTERM March 11, 2002, 9:55am–10:45am Your Name: Your TA: (circle one) Chris Alfeld Graham Jonaitis Andy Raich Joshua Rushton Fernando Miranda Score 1: 2: 3: 4: 5: Total: 1
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2 (1) Show how you can use the integral test to decide whether or not the series k =2 1 k ln k converges.
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3 (2) Compute the radius of convergence of the series X k =0 k + 1 3 k x 2 k = 1 + 2 3 x 2 + 3 9 x 4 + 4 27 x 6 + · · ·
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4 (3) Find the term containing
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Unformatted text preview: x 13 in the Taylor-Maclaurin series of f ( x ) = cos( x + π/ 6). 5 (4) If one replaces f ( x ) = ln(5 + x ) by f ( x ) ≈ ln 5 + 1 5 x-1 50 x 2 , then give an estimate for the error one makes, provided | x | < . 1. 6 (5) Find the general solution to the differential equation (1 + x ) dy dx = y 2 ....
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This note was uploaded on 08/08/2008 for the course MATH 222 taught by Professor Wilson during the Fall '08 term at Wisconsin.

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02spex2 - x 13 in the Taylor-Maclaurin series of f ( x ) =...

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