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Final

MATH 2B Study Guide - Final Guide: Trihydrogen Cation, 4DxExam


Department
Mathematics
Course Code
MATH 2B
Professor
All
Study Guide
Final

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MATH 2B: SAMPLE FINAL #1
This exam consists of 14 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. (6 points) Suppose that R1
1f(x)dx = 6,R4
1f(x)dx =2and R1
1h(x)dx = 9. Use this
information to compute the following.
a. R1
46f(x)dx
b. R1
12f(x) + 3h(x)dx
c. R4
1f(x)dx
2. (6 points)
a. Evaluate the following derivative
d
dx Zx2
sin(x)
t3tan(t)dt.
b. Let r(t)be the rate at which the world’s oil is consumed, where tis measured in years starting
at t= 0 representing January 1, 2000, and r(t)is measured in barrels per year. What does
R13
0r(t)dt represent and what are its units?

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3. (6 points) Evaluate Rx2tan1x dx
4. (6 points) Evaluate Z1
xln(3x)dx
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5. (6 points) Evaluate Rsin5(x) cos2(x)dx
6. (6 points) Evaluate Zx225
xdx, where x > 5
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