APPM 1350 Forgiveness midterm II Spring 2007
Books, notes and electronic devices are not permitted. Write your (1) name, (2)
instructor’s name and (3) recitation number on the front of your bluebook. Solve all
5 problems. Show your work clearly and box your answer. A correct answer with
incorrect or no supporting work may receive no credit, while an incorrect answer
with relevant work may receive partial credit.
1. (20 points)
(a) Is there a value of bthat would make the function
f(x) = ½x+b, x < 0
cos(x), x ≥0
differentiable at x= 0?
(b) Calculate: lim
x→0
tan(2x)
x
(c) Calculate: lim
x→−∞
x4+ 3x+ 1
x2+ 1
(d) Use implicit differentiatioin to find dy
dx in x2=x−y
x+y
2. (20 points)
A cop is trying to videotape a robber who has stolen a Porche. Unknown
to her, there is an automatic camera placed on a pole 132 ft above the ground
tracking her movements. The car is moving directly towards the pole at 264
ft/sec. What would the speed of the car with respect to the camera be when
the car is 30 ft from the base of the pole?
3. (20 points)
Consider the equation x=1
x2+ 1.
(a) Show that the equation has at least one solution in (0,1).
(b) Approximate this solution by using Newton’s method for x0= 1
(calculate only x1).
4. (20 points)
Consider the function f(x) = x2
x−1, for x6= 1.
(a) Find the xand ycoordinates of all local maxima and minima. Iden-
tify which are maxima and which are minima. Justify your answers.
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