quiz4Asol - Solutions to Quiz 4A...

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Unformatted text preview: Solutions to Quiz 4A www.math.ufl.edu/˜harringt February 9, 2008 1. Suppose that g (x) is a continuous function on [1, 2]. Furthermore, we know that g (1) < 0 and g (2) > 0. What does the Intermediate Value Theorem tell us? The Intermediate Value tells use that there exists a c (may not be unique) in the interval of (1, 2) such that f (c) = 0. NOTE: Since g (1) = 0 and g (2) = 0 then we know c ∈ (1, 2). If you put [1, 2] that will be acceptable for this quiz. 2. Evaluate the following limit: limx→−4 lim x→−4 1 4 1 +x = 4+x lim 1 1 +x 4 4+x . x+4 4x 4+x x+4 lim ÷ (4 + x) x→−4 4x x+4 1 lim x→−4 4x 4 + x 1 lim x→−4 4x 1 −1 = 4(−4) 16 x→−4 = = = = 3. Use the given graph of f to state the value of each quantity, if it exists. (b) limx→1+ f (x) = −3 (d) f (1) = −2 (a) limx→1− f (x) = 1 (c) limx→3 f (x) = 0 1 ...
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This note was uploaded on 07/10/2011 for the course MAC 2311 taught by Professor All during the Fall '08 term at University of Florida.

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