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AP Calculus BC Exam Preparation

ap calculus bc questions ap calculus bc test prep


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:2-Find the Taylor series expansion of
01-02 ap-calculus-bc questions

01-02-a ap-calculus-bc questions
Mark one answer:

A
B
C
D


Q:3-Find the Maclaurin Series of the function
f(x)=sinx
up to the fifth degree.

01-03-a ap-calculus-bc questions
Mark one answer:

A
B
C
D


Q:4-Find the interval of convergence for x of the Taylor Series
01-04 ap-calculus-bc questions

Mark one answer:

(-1/5,1/5)
(-∞,∞)
x=0
x=5
(-5,5)


Q:5-Determine whether the series converges or diverges:
01-05 ap-calculus-bc questions

Mark one answer:

The series is divergent.
The series may be convergent, divergent, or conditionally convergent.
The series is (absolutely) convergent.
The series is conditionally convergent.


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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 01-07 ap-calculus-bc questions 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?
01-09 ap-calculus-bc questions

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



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