LIMITS AT INFINITY

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CHAPTER 3

• SECTION 3.5
• LIMITS AT INFINITY

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What Happens?

• We wish to investigate what happens when
  functions go

To infinity and beyond
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Definition of Limits at Infinity and Figure 3.34
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Definition of a Horizontal Asymptote
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Theorem 3.10 Limits at Infinity
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Limits at Infinity
Theorem
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Limits at Infinity
NOTE f(x) may cross horizontal asymptotes near
zero.
Theorem
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Divide top bottom by the highest power in the
denominator.
This means the function has a SLANT (oblique)
asymptote.
To find where, do synthetic division and throw
out the remainder.
Oblique Asymptote at
remainder
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Because of a radical or an absolute value,
we must also check
Since x is a negative number,
f(x) has horizontal asymptotes at
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Guidelines for Finding Limits at /- infinity of
Rational Functions
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LETS LOOK AT THIS AGAIN---AND IT WILL BE
EASIER!!!!!!!!!!
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We cant narrow it down to a single value.
By the Squeeze Theorem
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Asymptotes Limits at Infinity

• For xgt0, xx (or my x-values are positive)
• 1/big little and 1/little big
• sign of denominator leads answer
• For xlt0 x-x (or my x-values are negative)
• 2 and 2 are HORIZONTAL Asymptotes

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Definition of Infinite Limits at Infinity
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Look!
This can be rewritten as
As
.
Therefore
,