MTH132-Test1 - sin 2 ) 2 cos( =-x x has a solution. Page 3...

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Page 1 10/18/2011 Name (Print Clearly): Student Number: Sept 15, 2008 Instructor: Dr. W. Wu Instructions: Answer the following questions in the space provided. There is more than adequate space provided to answer each question. The total time allowed for this quiz is 50 minutes. 1 [4 pts each] . Find the following limits. (a) 1 2 lim 2 2 0 - + - + x x x x x (b) x x x x x 3 6 lim 2 2 3 - - - (c) ) 2 cot( lim 0 x x x (d) x x x x x 3 6 lim 2 2 - - - (e) x x x x 3 6 lim 2 2 3 - - -
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Page 2 10/18/2011 2 [5 pts each] . If x x f / 1 ) ( = , please evaluate the limit of the form h x f h x f h ) ( ) ( lim 0 - + , (a) when . 4 = x (b) when . 0 x x = 3 [10 pts] . Please use the intermediate value theorem to show that the equation
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Unformatted text preview: sin 2 ) 2 cos( =-x x has a solution. Page 3 10/18/2011 4 [5 pts each]. Suppose 2 3 2--= x x y . (a) Find the asymptotes of this function. (b) Find the dominant terms and sketch the graph of this function. 5 [5 pts each]. At which points are each of the following functions continuous? (a) 2 1 2-+ + = x x x y Page 4 10/18/2011 (b) x x y cos 2 + = 6 [10 pts] . Use the Sandwich Theorem to find 3 ) 3 sin( lim 2 2-- x x x x ....
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MTH132-Test1 - sin 2 ) 2 cos( =-x x has a solution. Page 3...

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