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Unformatted text preview: Project 8
Consider the following piecewise deﬁned function for various choices of the numbers p and q . −p x < −1 x 2 x = −1 f (x) = 2−x −1 < x < 2 √ x+q x≥2 1. Sketch the graph of f (x) below with the choices p = 1 and q = 1. Determine whether f (x) is continuous from the right, left, both, or neither at x = −1, x = 0, and x = 2. Classify each discontinuity as inﬁnite, jump, or removable. 1 2. For what choices of p and q do the limits x→−1 lim f (x) and lim f (x) both
x →2 exist? Do these choices make f (x) continuous? Why or why not? Sketch the graph of f (x) below with these choices of p and q . If the function f (x) is 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? 2 ...
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This note was uploaded on 01/13/2010 for the course MAC 2311 taught by Professor All during the Fall '08 term at University of Florida.
- Fall '08