sample_midterm2_21c

# Sample_midterm2_21c - Calculus Math 21C Fall 2010 Sample Questions Midterm 2 1 Determine the interval of convergence(including the endpoints for

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Calculus : Math 21C, Fall 2010 Sample Questions: Midterm 2 1. Determine the interval of convergence (including the endpoints) for the following power series. State explicitly for what values of x the series con- verges absolutely, converges conditionally, and diverges. In each case, specify the radius of convergence R and the center of the interval of convergence a . (a) n =1 ( - 1) n 2 n n ( x - 1) n ; (b) n =0 1 3 n + 1 x 2 n ; (c) n =0 1 n 2 5 n (2 x + 1) n . 2. Let ⃗u = 2 i - j + 3 k, ⃗v = - i + 2 j + 2 k. Compute: (a) | ⃗u | ; (b) | ⃗v | ; (c) the angle θ between ⃗u , ⃗v (you can express it as an inverse trigonometric function); (d) the projection proj ⃗v ⃗u of ⃗u in the direction of ⃗v . 3. (a) Find the area of the triangle with vertices P ( - 2 , 2 , 0), Q (0 , 1 , - 1) and R ( - 1 , 2 , - 2). (b) Find a parametric equation for the line in which the planes 3 x - 6 y - 4 z = 15 and 6 x + y - 2 z = 5 intersect. 4.

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## This note was uploaded on 11/17/2010 for the course MAT 21C NA taught by Professor Na during the Fall '01 term at UC Davis.

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Sample_midterm2_21c - Calculus Math 21C Fall 2010 Sample Questions Midterm 2 1 Determine the interval of convergence(including the endpoints for

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