Name

15. (8.4) The improper integral

Z 1

0

sin(t)

t

dt converges, but its value cannot be computed

exactly because sin(t)t

has no elementary antiderivative. It is also di�cult to estimate

with standard methods due to the fact that sin(t)t

is undefined at t = 0.

(a) Approximate the value of the integral using a degree 5 Taylor polynomial forsin(t).

(b) The actual value of the integral is 0.94608.... How accurate was your estimate?(Hint: If your answer is grossly inaccurate, you did the previous part of thequestion incorrectly.)

Math 121 - Winter 2015 Homework - Occhipinti20

Name

16. (10.1) Write down decimal approximations for several terms of the sequencea

n

=�

n

n+1

�n

. Does the sequence appear to be converging? If it converges, try tofigure out what it converges to accurate to 4 decimal places. (Feel free to use WolframAlpha.)

Math 121 - Winter 2015 Homework - Occhipinti21