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Math 21CName:Spring 2017Practice Midterm 205/11/2017Time Limit: 50 MinutesTeaching AssistantThis exam contains 7 pages (including this cover page) and 11 questions. Youmustshowyour work and justify your answer. When you apply a convergence test, youmustname theconvergence test, and explicitly check the assumptions of that convergence test. You maynotuse any books, notes, calculators, or any other electronic devices.Read each question carefully.QuestionPointsScore152535455565758595105110Total:50
Math 21CPractice Midterm 2 - Page 2 of 705/11/20171. (5 points) Use the definition of Taylor series to find the Taylor series off(x) =1√xatx= 1.2. (5 points) Use power series operations to find the Taylor series off(x) =sin(x2)x2atx= 0.
Math 21CPractice Midterm 2 - Page 3 of 705/11/20173. (5 points) Find the Taylor polynomialP2(x) of order 2 for the functionf(x) = arctanxatx= 0. Use the remainder estimation theorem to estimate the error|arctan(x)-P2(x)|for|x|<1.