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Learn about infinite limits where f(x) increases or decreases without bound, and vertical asymptotes when f(x) approaches infinity. Explore the properties of infinite limits and how to find them in calculus problems.
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September 11th, 2017 INFINITE LIMITS (1.5)
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.
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.
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.
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.
