Department

MathematicsCourse Code

MATH 2BProfessor

AllStudy Guide

FinalThis

**preview**shows pages 1-2. to view the full**7 pages of the document.**MATH 2B: SAMPLE FINAL #2

•This exam consists of 13 questions and 100 total points.

•Read the directions for each problem carefully and answer all parts of each problem.

•Please show all work needed to arrive at your solutions (unless instructed otherwise). Label

graphs and deﬁne any notation used. Cross out incorrect scratch-work.

•No calculators or other forms of assistance are allowed. Do not check your cell phones

during the exam.

•Clearly indicate your ﬁnal answer to each problem.

1. (8 points) Consider continuous functions fand f′(where f′denotes the derivative of f) with

values given by the following table:

x0 1 2 3 4 5

f(x) 3 4 6 9 13 18

f′(x) 1 2 4 6 7 5

a. Find R4

0f′(x)dx

b. Estimate R4

1f(x)dx Using a left-hand Riemann sum with 3 equal subintervals.

c. Evaluate the following derivative at the point x= 3

d

dx Zx

2

f(t)dt

d. Suppose f(x)gives the height of a rocket, measured in yards, xminutes after its launch.

What are the units of R4

0f′(x)dx and what does this quantity represent.

2. (7 points) Evaluate Zx

1 + x4dx

Only pages 1-2 are available for preview. Some parts have been intentionally blurred.

3. (7 points) Evaluate Zx2

e2xdx

4. (7 points) Evaluate Rsin3(4t)dt

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