exam3a - Math 151 Section 16 Exam 3 Tuesday Name Please...

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Math 151, Section 16 Exam 3 Tuesday, November 23, 2010 Name: Please read and sign the following academic integrity pledge. I pledge on my honor that I have not given nor re- ceived any unauthorized assistance on this exam. Signature Do all parts of the following problems. You are NOT allowed to use a calculator or computer. You must show your work to receive credit. 1
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1. Compute each of the following limits, provided it exists. If a particular limit does not exist, write DNE. If a particular limit is + or -∞ , state this instead of writing DNE. You must show your work to receive credit. (18 points) (a) lim x 0 x tan( x ) (b) lim x →∞ x 2 e x (c) lim x 0 + x 2 x 2
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2. Determine the x and y coordinates of all absolute minima and all absolute maxima of the function f ( x ) = x + 3 x 2 / 3 on the interval [ - 1 , 8]. (7 points) 3. Let f ( x ) = 3 x x 2 + 9 . (a) Find all intervals on which the graph of f is increasing; on which the graph of f is decreasing. (4 points) (b) Find the x and y coordinates of all local extrema of f . Be sure to specify which correspond(s) to a local minimum, and which to a local maximum. (4 points) 3
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