Answers to EvenNumbered HW  Test 2
HW #7  13
HW 7
p. 96
2.
lim
x
→
1

f
(
x
) = 3 means we can make
f
(
x
) as close to 3 as we like by taking
x
sufficiently
close to 1 from the left, but not equal to 1.
lim
x
→
1+
f
(
x
) = 7 means we can make
f
(
x
) as close
to 7 as we like by taking
x
sufficiently close to 1 from the right, but not equal to 1. The
(twosided) limit lim
x
→
1
f
(
x
) does not exist (DNE) since the left hand limit is not equal to the
righthand limit.
4. (a) 2; (b) 4; (c) 2; (d) DNE; (3) 3.
6. (a) 4; (b) 4; (c) 4; (d) undefined; (e) 1; (f) 1; (g) DNE; (h) 1; (i) 2; (j) undefined; (k) 3;
(l) DNE; this is because we
can’t
make
f
(
x
) as close as we like to some number
L
by taking
x
sufficiently close to 5 from the left, but not equal to 5. A reasonable guess for
L
would be
4, but if we want
f
(
x
) within 0.5 of 4, you can see no matter how close we make
x
to 5 from
the left, some values of
f
(
x
) will always overshoot the range (3
.
5
,
4
.
5).
8. (a)
∞
; (b)
∞
; (c)
∞
; (d)
∞
; (e)
x
=

3;
x
= 2;
x
= 5.
14. There are many correct answers. Just draw little sections of the graph with each one
satisfying a stated condition.
You don’t even have to connect up the different sections,
although that would give a more typicallooking function.
26. To see that this is an infinite limit, just substitute

3 in the numerator and denominator:

1
0
is infinite. To get the right sign, substitute a value of
x
slightly to the left of

3. The
denominator will be negative, and the numerator will be close to

1. The two negatives give
(positive)
∞
.
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 '10
 Vartanian,Michael
 Limit, Limit of a function, 4 mile, THMs

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