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Unformatted text preview: Name Homework 1
Sections 1.7 & 1.8 Be sure to use the denition of continuity for number 4 (i.e. there should be some limits).
1. (6) Given lim f (x) = 4, lim g (x) = −2 and h(3) = 5, compute the following, if possible.
x→3
x→3
Show your use of the properties of limits. If it is not possible to compute one of the
following, explain why not.
(a) lim (xf (x)) (c) lim (h(x)f (x)) (g (x))2
(b) lim
x→3 f (x) (d) lim (f (x) + 2) x→3 x→3 x→3 2. (4) Find a value of the constant k so that the following limit exists. Hint: What
feature(s) of the graph of the rational function would make the limit exist or not exist?
x2 − kx + 6
x→2
x−2
lim 3. (4) For each of the following, give an example of a function with the properties described. [1pt for a graph, 2pts for a function in formula form]
(a) Continuous on [0, 1] but not continuous on [1, 3]. ecx 4. (6) Consider the function f (x) = (x + c)2 2x + 6c
f (x) is continuous? (b) Strictly increasing but not continuous
on [0, 10]. x<0
0 ≤ x < 2 . Is there a constant c so that
x≥2 ...
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 Spring '08
 KENNEDY
 Continuity, Limits

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