MATH 131 Midterm: MATH 131 UMass Amherst 131f16 Exam 1

• School: UMASS-Amherst
• Department: Mathematics
• Course: MATH 131
• Professor: All

Document Summary

1 e x2 dx using the taylor polynomial with n 3. Note that taylor series for e x 1 x 1. So, e x2 1 x2 1. Hence, the taylor polynomial with n 3 is 1 x2. Thus, x6 . x4 1 x2 1. 3! x3 , for all x. Problem 2 (7 points) use a taylor series to compute limx 0 cos x2 1 x4 cos x 1 1. 6! x6 . cos x2 1 1. Hence, cos x2 1 x4 lim x 0. 6! x8 1. 6! x4 x6 1 x4 x2 1 x4. 6! x4 1.