Math 155-004, Quiz 10
April 5, 2009
NAME:
Instructions: You may use calculators. Work that is erased or crossed out will not be graded.
1. For f (x) = 200 ln(x) + x−2 + 2000e−x , find f0 (x) and f∞ (x).
2
2x
2. For f (x) = 4+x
2 , find f0 (x) and f∞ (x). Use the Method of Matched Leading Behaviors to sketch a graph
of f (x) on the interval [0, ∞).
3. Evaluate the following limits. If you use leading behavior, show each step. If you use L’Hopital’s Rule,
justify its use and show each step.
(a) limx→0
tan x
x+ex −1
(b) limx→∞
(c) limx→3
x2 +ex
ln(x)+e5x
sin(x−3)
x−3