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INFINITE LIMITS (1.5)

September 11th, 2017. INFINITE LIMITS (1.5). I. INFINITE LIMITS.

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INFINITE LIMITS (1.5)

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  1. September 11th, 2017 INFINITE LIMITS (1.5)

  2. I. INFINITE LIMITS Def: An infinite limit is a limit in which f(x) increases or decreases without bound as x approaches c. Although we may assign the values of infinity or negative infinity for these limits, the limits still fail to exist because they lack a real number value.

  3. II. VERTICAL ASYMPTOTES Def: If f(x) approaches infinity (or negative infinity) as x approaches c from the right or left, then the line x=c is a vertical asymptote of the graph of f.

  4. Thm. 1.14: Vertical Asymptotes: Let f and g be continuous on an open interval containing c. If and there exists an open interval containing c such that for all in the interval, then the graph of the function given by has a vertical asymptote at x=c.

  5. Thm. 1.15: Properties of Infinite Limits: Let c and L be real numbers and f and g be functions such that • and • 1. Sum or difference: • 2. Product: • 3. Quotient: • Similar properties hold for one-sided limits and for functions for which the limit as x approaches c is negative infinity.

  6. Ex. 1: Find each limit.

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