MATH 152 Activity 13 (Section 10.7-10.9)
Directions: Put both your name and your partners name on the answersheet. Use scratch paper for work, meaning only
put the answers on the answer sheet. Turn in only ONE answer sheet per pair. Calculators are allowed and you may
use your notes and textbook. Failure to follow these instructions will result in a 1 point deduction. Neat handwriting is
expected.
1. Find the Taylor Series expansion for f (x) = ln(x + 1) at x = 2.
2. Use a Maclaurin series derived in this section to obtain a Maclaurin series for f (x) = x sin(x3 ).
3. Use a Maclaurin series derived in this section to obtain a Maclaurin series for f (x) =
e2x
.
x2
∞
X
5(−2)n+1
4. Find the sum of the series
n!
n=0
5. Use a Maclaurin series derived in this section to obtain a Maclaurin series for f (x) = cos
6. Evaluate
7. Write
error.
Z
Z
4
.
sin(x6 ) dx as an infinite series.
1
sin(x2 ) dx as a series. Add the first 3 terms of this series to approximate
0
8. Let f (x) =
x
Z
1
sin(x2 ) dx and estimate the
0
√
x.
(i) Find T2 (x), the second degree Taylor polynomial, at x = 4
(ii) Use Taylor’s Inequality to estimate the error in using T2 (x) to approximate f (x) for 3.5 ≤ x ≤ 4.2.
1