MAC 2233/001006 Business Calculus, Fall 2011
CRN: 81700–81702, 81705, 81716, 81715
Assistants
: Matthew Fleeman, Arbin Rai, Tadesse Zerihun, Vindya Kumari, Junyi Tu, Jing
han Meng
Notes on finding limits at infinity and infinite limits
On finding infinite limits
.
Suppose that we have a function
h
(
x
) =
f
(
x
)
g
(
x
)
(so that
f
(
x
) is the
numerator (top) and
g
(
x
) is the denominator (bottom)) and that we need to consider the limit
of
h
(
x
) as
x
→
c
. As before, there are three cases:
(1) if
g
(
c
)
negationslash
= 0 then substitution works, and we have a (finite) limit.
(2) if
g
(
c
) = 0 and
f
(
c
)
negationslash
= 0 then the limit does not exist, and we say we have an “infinite
limit” (and see example below for determining the sign).
(3) if
g
(
c
) =
f
(
c
) = 0 then more work is needed.
Example
. Determine if the limit lim
x
→
1
+
2+
x
1

x
exists, and if not, say if it is +
∞
or
−∞
.
Solution.
When
x
= 1, we see that the top is nonzero but the bottom is zero. Hence we have
an infinite limit. To see if the limit is +
∞
or
−∞
(and sometimes it is neither), we note that
as
x
→
1
+
(that is,
x >
1 and
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 Fall '08
 DANIELYAN
 Calculus, Limits, Limit, lim, Bottom

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