Limits At Infinity, Infinite Limits - University of Utah · 4B Limits at Infinity 5 Definition: (Infinite limit ) We say if for every positive number, m there is a corresponding δ

4B Limits at Infinity

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Limits At Infinity, Infinite Limits

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

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 .

4B Limits at Infinity

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EX 3

EX 4

EX 5

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

4B Limits at Infinity

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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: