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Calculus practice problems
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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