1.5 Infinite Limits

# 1.5 Infinite Limits - has a vertical asymptote at x = c ≠...

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Infinite Limits Section 1.5

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Defn. of Vertical Asymptote If f(x) approaches infinity (or negative infinity) as x approaches c from the right or the left, then the line x = c is a vertical asymptote of the graph of f. Look at Defn. of Infinite Limits pg. 79
Thm. 1.14 Vertical Asymptotes Let f and g be continuous on an open interval containing c . If f(c) 0, g(c) = 0, and there exists an open interval containing c such that g(x) 0 for all x c in the interval, then the graph of the function given by

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Unformatted text preview: has a vertical asymptote at x = c . ≠ ≠ ≠ ) ( ) ( ) ( x g x f x h = Thm. 1.15 Properties of Infinite Limits Let c and L be real numbers and let f and g be functions such that 1. Sum or Difference: ∞ = → ) ( lim x f c x and x c lim g( x) L → = [ ] ∞ = ± → ) ( ) ( lim x g x f c x 2. Product: 3. Quotient: [ ] , ) ( ) ( lim ∞ = → L x g x f c x [ ] , ) ( ) ( lim <-∞ = → L x g x f c x ) ( ) ( lim = → x f x g c x...
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1.5 Infinite Limits - has a vertical asymptote at x = c ≠...

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