21C MT2 Study

21C MT2 Study - Co-21C Midterm 2 Review Problems 1) Find...

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Co-21C Midterm 2 Review Problems 1) Find the interval of convergence for the power series ( ! 1) n ( x ! 2) n n 4 n n = 1 " # . Be sure to check endpoints! 2a) Find the 1 st four terms of the Taylor series for f ( x ) = 1 x 2 centered at a = 3. b) Find the n th degree Taylor series expressed in summation notation. 3) Use the 1 st 4 terms of the Maclaurin series for e x to approximate each value. Then put an upper bound on the error. a) 1 e b) e 3 *Note: Use the fact that e < 27 8 (why did I choose that fraction?) 4) Use the known Maclaurin series for sin x to approximate x sin x 3 dx 0 1 ! to within 1 1000 . 5) Consider the vectors: u ! = 5 i + j and v ! = ! i + 3 j . Sketch and find each of the following: a) u ! + v ! b) v ! ! u ! c) comp v u d) proj v u e) orth v u 6) Find a unit vector orthogonal to u = i – 2 j + 3 k. 7) Find the parametric equation of the line that is perpendicular to the plane x + 2 y ! 3 z = ! 4 , intersecting it at (4, 5, 6). 8) Consider the three points in space: P(1, 2, 3), Q(6, 5, 4) and R(-2, 0, 1). a) Find the equation of the plane that passes through the points.
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21C MT2 Study - Co-21C Midterm 2 Review Problems 1) Find...

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