3.5 Limits at Infinity
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1
x
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1
Technique for finding limits at infinity...
divide all terms by x with highest exponent
3 - 2x
3x3 - 1
3 - 2x
3x - 1
3 - 2x2
3x - 1
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Definition of a Horizontal Asymptote:
The line y = L is a horizontal asymptote if:
f(x) = L
or
f(x) = L
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2
Oct 5­12:29 PM
Shortcut...
bottom heavy (degree of numerator < degree of denominator)...
top = bottom
top heavy
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3
5x3/2
4x2 + 1
5x3/2
4x3/2 + 1
5x3/2
4√x + 1
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Non Rational Functions
may approach different values at -∞ and ∞
short cut rules do not apply
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4
Your Turn!
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Trigonometric Limits
sin x
sin x
x
sin 3x
x
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5
Find the Limit.
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EXIT
TICKET
1.
(A) 4
(B) 1
(C) 1/4
(D) 0
(E) -1
2. When don't the "top heavy / bottom heavy" shortcuts work?
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