MTH132-Test1

# MTH132-Test1 - x x sin 2 2 cos = has a solution in 2 π...

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Page 1 10/18/2011 Name (Print Clearly): Student Number: Feb. 2, 2009 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 [5 pts each] . Find the following limits. (a) 1 cos 2 lim 2 2 0 - + - + x x x x x (b) x x x x x 3 6 lim 2 2 3 - - - (c) x x x x x 3 6 lim 2 2 - - - (d) x x x x 3 6 lim 2 2 3 - - -

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Page 2 10/18/2011 (e) ) 3 cot( lim 0 x x x 2 [5 pts each] . If x x f 2 ) ( = , please evaluate the limit of the form h x f h x f h ) ( ) ( lim 0 - + , (a) when 2 = 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: x x sin 2 ) 2 cos( = has a solution in ] 2 / , [ π . Page 3 10/18/2011 4. Suppose 2 5 2--= x x y . (a) [4 pts]. Use polynomial division to decompose this rational function into a polynomial and a remainder. (b) [6 pts]. Find the vertical asymptote and oblique asymptote of this function by evaluating limits. 5 [5 pts each]. At which points are each of the following functions continuous? (a) 6 4 2 2---= x x x y Page 4 10/18/2011 (b) x x y cos 2 + = 6 [5 pts] . Use the Sandwich Theorem to find x x x ) cos( lim 2 ∞ → ....
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MTH132-Test1 - x x sin 2 2 cos = has a solution in 2 π...

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