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Unformatted text preview: r x is defined for all x , then 1 lim = r x x Application: Suppose that the diameter of an animals pupils is given by ) ( x f mm, where x is the intensity of light on the pupils. If 15 4 90 160 ) ( 4 . 4 . + + = x x x f , find the diameter of the pupils with maximum light. [Source: Calculus: Concepts & Connections by R. Smith and R. Minton, 2006] Example: 9 5 2 7 lim 2 2 + x x x x MATH1010: Chapter 2 cont 3 Note: Our strategy for infinite limits of rational functions is to divide by the largest power in the denominator ! Example: 7 3 1 5 lim 2 x x x Example: 6 3 6 2 4 3 8 7 5 2 lim x x x x x + Example: 4 2 5 lim 2 + x x x What happens if we instead consider the limit as x ? i.e. 4 2 5 lim 2 + x x x Example: 2 3 6 3 lim 2 2 + x x x Example: 6 8 lim x x x...
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 Spring '08
 Kim
 Calculus, Asymptotes, Derivative, Limits

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