MATH 141 Midterm: MATH141 BOYLE-M FALL2009 0101 MID EXAM 3

• School: University of Maryland
• Department: Mathematics
• Course: MATH 141
• Professor: All

Document Summary

Math 141 fall 2009 boyle exam 4. Put a box around the nal answer to a question. Compute the sum of the series p n=2 3(1/4)n : (a) (10 pts. ) Find the polynomial of degree at most 15 which gives the best approximation to the function f (x) = 5 cos(x3) for x near zero. If a power series converges at x = 1, then the power series converges at x = 1. (c) (5 pts. ) Every polynomial with real coe cients is a product of poly- nomials of degree at most two with real coe cients: determine whether the following series converge. Name a test which justi es your answer. (a)(10 pts. ) N8 + n5 + 2: write the following complex numbers z in the form a + ib with a and b real numbers. (a)(7 pts. ) 3 + 4i (b)(7 pts. ) (1+i)6 (c)(6 pts. )