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