Test 4 Form A
MA141-008
November 21, 2011
Stephen Adams
North Carolina State University Department of Mathematics
Please put all work in the stamped blue book that has been provided. Nothing on this test
sheet will be graded. Please put one problem on each page; you are allowed to use the back of the
sheet as a new page. No calculators, formula sheets, or other aids are permitted. Please show all
of your work. Simplify all solutions completely and clearly indicate your answers.
1. (a) [5 pts.] Explain why Newton’s method doesn’t work for finding the root of the equation
y = x3 − 12x + 36 if the initial approximation is chosen to be x1 = −2.
(b) [5 pts.] How might you fix the problem that occurs in part (a)?
2. A car is stopped at a red light on a road where the speed limit is 45 miles per hour. As soon
as the light turns green, the car starts at a constant acceleration of 10 feet per second per
second.
(a) [5 pts.] How long does it take for the car to travel 180 feet?
(b) [5 pts.] Is the car speeding once it has traveled 180 feet? Justify your answer. [HINT:
The speed limit of 45 miles per hour is equivalent to 66 feet per second.]
3. A particle moves along a line so that its velocity at time t is v(t) = t2 − 9t + 7.
(a) [5 pts.] Write a single integral that will give the displacement of the particle during the
time period 0 ≤ t ≤ 4. DO NOT EVALUATE THE INTEGRAL!
(b) [5 pts.] Write a single integral that will give the distance traveled by the particle during
the time period 0 ≤ t ≤ 4. DO NOT EVALUATE THE INTEGRAL!
(c) [5 pts.] Do your integrals from parts (a) and (b) give the same number? Justify your
answer without evaluating the integrals.
" #
n
X
i 7 1
4. [10 pts.] Evaluate: lim
·
n→∞
n
n
i=1
5. Evaluate the following integrals:
Z
√
(a) [10 pts.]
x3 − 3 x − 3 dx
Z
π/2
(b) [10 pts.]
x cos x dx
0
Z
1
2
xex dx
(c) [10 pts.]
0
Z
1
(1 − |x|) dx
(d) [10 pts.]
−1
6. (a) [10 pts.] State the First Fundamental Theorem of Calculus.
Z 3
d
3
(b) [10 pts.] Evaluate:
t sin t dt
dx
x