4B Limits at Infinity
Limits At Infinity, Infinite Limits
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4B Limits at Infinity
Definition: (Limit as
)
c∈ℜ
is defined on
We say that if for every
for
there is a corresponding number,
such that
then
m
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4B Limits at Infinity
EX 1
EX 2
Intuitively (looking at the graph) determine these limits.
Show that if n is a positive integer, then
.
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4B Limits at Infinity
EX 3
EX 4
EX 5
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4B Limits at Infinity
Definition: (Infinite limit )
We say
if for every positive number, m
there is a corresponding δ > 0 such that
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4B Limits at Infinity
EX 6
Determine these limits looking at this graph of
Ex 7
Find the horizontal and vertical asymptotes for this function,
.
then write a few limit statements including ∞.
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4B Limits at Infinity
Ex 8
a) Find the vertical and horizontal asymptotes for this function.
b) Determine these limits:
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4B Limits at Infinity
Determine these limits:
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