APPM 1350 EXAM 1 SUMMER 2009
On the front of your bluebook write: (1) your name, (2) your student ID number, (3) your in-
structor’s name, and (4) a grading table. You must work all of the problems on the exam. Show
ALL of your work in your bluebook and BOX in your final answers. A correct answer with no
relevant work may receive no credit, while an incorrect answer accompanied by some correct work
may receive partial credit. Textbooks, class notes, calculators, flying monkeys, and crib sheets are
NOT permitted. Please start each new problem on a new page of the bluebook.
1. (21 points) For each of the following, answer either TRUE or NOT NECESSARILY TRUE.
No justification is necessary.
(a) The points (2,5), (4,10), and (-3,−15
2) lie on the same straight line.
(b) If fis odd and gis odd, then f
gis odd.
(c) There is an xfor which cos2x+ 1 = π
2.
(d) If the velocity v(t) of a particle is increasing, the particle is speeding up.
(e) All polynomials are continuous functions.
(f) If tan φ=−1
√3, then φ=−π
6.
(g) If 2
|x−2|<1 then |x|>4.
2. (18 points) Evaluate each of the following limits, if it exists. If the limit does not exist, state
this and state your justification.
(a) lim
θ→0−
csc(2θ)
θ
(b) lim
s→0
1/√1 + s−1
s
(c) lim
x→−2
√x2+ 4x+ 4
(x+ 2)
3. (11 points)
(a) State the conditions necessary for f(x) to be continuous at the point x=c.
(b) Determine the values of band cso that the following function is continuous:
f(x) = x+ 1,1< x < 3
x2+bx +c, |x+ 2| ≥ 1
4. (11 points)
(a) State the definition of d
dx f(x).
(b) Use the definition to find d
dx√x+ 1.
THE EXAM IS CONTINUED ON THE BACK
