Q:1-Let P₅(x) be the fifth-degree Taylor polynomial approximation for f(x)=sin(x), centered at x=0.
What is the Lagrange error of the polynomial approximation to sin(1)?
Mark one answer:
1/7!
1/6!
0
1/5!
1

Q:6-Calculate the sum of a geometric series with the following values: n=15, a₁=4, r=1/3. Round the answer to the nearest integer.
Mark one answer:
8
6
10
7

Q:7-Which of the following tests will help determine whether is convergent or divergent, and why?
Mark one answer:
Root Test: Since the limit as x approaches to infinity is zero, the series is convergent.
Divergence Test: Since limit of the series approaches zero, the series must converge.
Integral Test: The improper integral determines that the harmonic series diverge.
P-Series Test: The summation converges since p=1.
Nth Term Test: The series diverge because the limit as xx goes to infinity is zero.

Q:8-Write out the first three terms of the Taylor series about a=1 for the following function:
f(x) = 10x² + x
Mark one answer:
11 + 21(x-1) + 10(x-1)²
0 + 21(x-1) + 10(x-1)²
11 + 21x + 10x²
0 + 0 + 0

Q:9-Determine whether the following series converges or diverges. If it converges, what does it converge to?

Mark one answer:
3/4
1
Diverges
4/3

Q:10-Calculate the sum, rounded to the nearest integer, of the first 16 terms of the following geometric series:
6 + 12.6 + 26.46 + 116.6886 + 245.04606 ...
Mark one answer:
780295
780300
780310
780305