APPM 1350 EXAM 2 SUMMER 2006
On the front of your bluebook write: (1) your name, (2) your student ID number, and (3) a
grading table. You must work all of the problems on the exam. SHOW ALL 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. Text books, class notes, calculators and crib sheets are NOT permitted. Please start each
new problem on a new page of the bluebook.
1. (25 points) Using the appropriate rules of differentiation, find the derivatives of the following
functions. No simplification is necessary. Show all your work.
(a) g(y) = ysin 1
y
(b) s(r) = tan2r3
(c) f(x) = s1 + tan x+1
x
(d) p(t) = "1 + 2
t−1
+ 3t#2
(e) h(x) = sin (sec (cos x))
2. (20 points) Evaluate each of the following limits, if it exists. If the limit does not exist, state
this and state your justification. If the limit goes to ±∞, find the dominant terms as it does
so. Show all your work.
(a) lim
t→∞
3t3/4+t5/6+t2
4t7/3+2
5√t
(b) lim
x→−∞
|x+ 3|
(x+ 3)
(c) lim
r→∞ pr2+ 1 −r
(d) lim
y→−∞
y3
y2+ 1
3. (15 points) Consider the curve called the conchoid of Nicomedes described by the equation
x2y2= (y+ 1)2(4 −y2)
(a) Find dy
dx .
(b) Find the tangent to the conchoid at the point (0,-2).
4. (20 points) Plot the function f(x) = 2 cos x+ sin 2xfor 0 ≤x≤2π. Find and label all critical
points, local and absolute extrema, and inflection points.
THE EXAM IS CONTINUED ON THE BACK
