APPM 1345 Exam 1 Spring 2011
INSTRUCTIONS: Books, notes, and electronic devices are not permitted. Write (1) your name,
(2) section number, and (3) a grading table on the front of your bluebook. Start each problem on
a new page. Simplify your answers. A correct answer with incorrect or no supporting work may
receive no credit, while an incorrect answer with relevant work may receive partial credit. Unless
otherwise indicated, show all work.
1. (15 points)
(a) Write in expanded form:
4
X
i=1
xi
i+ 1.
(b) Write in sigma notation: S=1
2−3
4+9
6−27
8+81
10.
(c) Find the value of
10
X
i=1
(2i2−2i−6).
(Hint: You may use the formulas at the end of the test.)
2. (10 points) Use Newton’s Method with an initial approximation of x1= 0 to find x3, the
third approximation to the root of the equation 2x3= 1 −x.
3. (10 points) Estimate the area under the graph of f(x) = 3
x4+ 1 from x= 2 to x= 4
using four approximating rectangles of uniform width and midpoint values. Leave your
answer unsimplified.
4. (10 points) Evaluate the following indefinite integrals.
(a) Z−2x2+ 3x−5√x+ 1
√xdx =
(b) Z2
3csc xcot x+ 2 sec2x
2dx =
5. (15 points) Use geometry to evaluate the following definite integrals.
(a) Z10
2
t
2dt =(b) Z1
−2
(5|x| − 10) dx =(c) Z9
−93−p81 −x2dx =
