MATH 2B Final: MATH 2B Final Exam 2Exam
Course CodeMATH 2B
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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
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. 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
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3. (7 points) Evaluate Zx2
4. (7 points) Evaluate Rsin3(4t)dt
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