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Mathematics 106 — Calculus II
Exam 1
February 6, 2009
Your Name:
There are 6 problems in this exam. On each problem, you must show all your work, or otherwise thoroughly explain your conclusions. There is always at least one step preceding a final answer. Units may be requested for your final answer; a point deduction will apply if they are omitted.
On the portion of the exam marked N C, you will be allowed 20 minutes during which your calculator must be closed and put away. If you finish this section early, you may hand in your work early. However, only after you hand in the ”no calculators” section will you be permitted to use a calculator.
You will have 55 minutes to complete this exam.
Question Point Value Your Score
No Calc. 50
Total 150
N C P
Math 106-C (Salomone) Exam 1 Show all your work!
Name:
Score (50 possible):
Problem 1-NC. (20 points) Use the Fundamental Theorem of Calculus to evaluate the following integrals:
(a) (10 points)
x
x
) 2 dx
(b) (10 points)
0
ee
x+x dx
Math 106 Exam 1 Score this page: Problem 1. (30 points) You design a camping tent whose footprint is a 10-foot-diameter circle and whose carbon- fiber frame is designed of rigid squares.
The tent... ...and a view of its^ square^ cross sections.
Calculate the exact volume this tent encloses, in cubic feet.
Math 106 Exam 1 Score this page: Problem 2. (35 points) Consider the initial-value problem
dy dx
4 y 1 + x^2
y(0) = 1.
(a) (15 points) Use Euler’s method with step size ∆x = 0. 25 to approximate y(1), and indicate what you’ve done on the slope field at left. Be sure to circle your final answer.
(b) (20 points) Use separation of variables to find the exact function which solves this IVP. How well does your answer to part (a) compare with the exact value of y(1)?
