P09Ans - Project 9 MAC 2233 1. Consider the following...

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Unformatted text preview: Project 9 MAC 2233 1. Consider the following piecewise defined function for various choices of constants p and q . Sketch its graph in the case that p = q = 1. −p x < −1 x 2 x = −1 f (x) = 2−x −1 < x < 2 √ x+q x≥2 Determine whether f (x) is continuous at x = −1, x = 0, and x = 2. Classify each discontinuity as infinite, jump, or removable. jump discontinuities at x = −1, 2 continuous at x = 0 2. For what choices of p and q do the limits lim f (x) and lim f (x) both exist? Do these x→−1 x→2 choices make f (x) continuous? Why or why not? Sketch the graph of f (x) with this p and q . p = 3 and q = −2 If the function f (x) is now still not continuous at some point, can it be redefined to make it continuous at that point, without altering the behavior of f (x) near the point? If so, how? What do we call this type of discontinuity? f (−1) = 3 removes the ”hole” at x = −1 Evaluate the limits at infinity for the function f (x). limit as x → ∞ is ∞ limit as x → −∞ is 0 ...
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This note was uploaded on 12/27/2011 for the course MAC 2233 taught by Professor Smith during the Spring '08 term at University of Florida.

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