Math 111 – Calculus 1 Practice Problems for Exam 3 Fall 2008
1. Find the extreme values of f(x) = (x2−2x)3on the interval [−1,3].
(a) local maxima: minima:
(b) absolute maximum: minimum:
2. Evaluate the following limits, where possible. (Hint: Determine whether the limit has
an indeterminate form before doing any calculations.)
Clearly indicate every application of L’Hospital’s Rule!
(a) lim
x→0
sin x−x
x3
(b) lim
t→0(sec x−tan x)
(c) lim
x→∞
x2e−x
(d) lim
x→0x2ln x2
(e) lim
t→∞
t−ln t
(f) lim
x→0
2x−1
x
(g) lim
x→0
arcsin x
x
(h) lim
x→1
(ln x)2
x
3. Let f(x) = 4(x+ 1)
(x+ 2)2.
(a) Find the xand yintercepts of f.
(b) Find the vertical and horizontal asymptotes of f.
(c) Find the intervals on which fis increasing or decreasing.
(d) Find all the points at which fhas a local maximum or a local minimum.
(e) Determine the intervals on which fis concave up or concave down, and find the
inflection points.
(f) Sketch the graph of f. Be sure to label all the xand yvalues of the intercepts,
local maxima, local minima, inflection points, and asymptotes.
4. Let f(x) = (x2−2x+ 2)ex. Repeat problem3
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