# practice_midterm_2 - Math 21C Spring 2017 Practice Midterm...

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Math 21C Name: Spring 2017 Practice Midterm 2 05/11/2017 Time Limit: 50 Minutes Teaching Assistant This exam contains 7 pages (including this cover page) and 11 questions. You must show your work and justify your answer. When you apply a convergence test, you must name the convergence test, and explicitly check the assumptions of that convergence test. You may not use any books, notes, calculators, or any other electronic devices. Read each question carefully. Question Points Score 1 5 2 5 3 5 4 5 5 5 6 5 7 5 8 5 9 5 10 5 11 0 Total: 50
Math 21C Practice Midterm 2 - Page 2 of 7 05/11/2017 1. (5 points) Use the definition of Taylor series to find the Taylor series of f ( x ) = 1 x at x = 1. 2. (5 points) Use power series operations to find the Taylor series of f ( x ) = sin( x 2 ) x 2 at x = 0.
Math 21C Practice Midterm 2 - Page 3 of 7 05/11/2017 3. (5 points) Find the Taylor polynomial P 2 ( x ) of order 2 for the function f ( x ) = arctan x at x = 0. Use the remainder estimation theorem to estimate the error | arctan( x ) - P 2 ( x ) | for | x | < 1.
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