MTH132-Test3

# MTH132-Test3 - (c Find all local extrema(types and values...

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Page 1 10/18/2011 Name (Print Clearly): Student Number: April 3, 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 [3 pts each] . Find limits of each of the following functions. (a) 1 1 lim 3 / 1 5 / 3 1 - - x x x (b) ) 2 csc( lim 0 x x x (c) x x x x x x sin 3 2 lim 2 2 + - (d) | 1 | 1 lim 1 - - + x x x

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Page 2 10/18/2011 2. [5 pts each] . Find indefinite integrals. (a) - + - dx x x x ) cos 2 3 ( 2 3 / 1 (b) + dr r 2 ) 5 2 ( 1 3. [8 pts]. Solve initial value problem: 1 ) 0 ( ), sin( = = y x dx dy π . 4. [10 pts] . Let , 1 ) ( x x x f + = ] 2 , 2 1 [ . (a) Show that f(x) satisfies the hypotheses of the Mean Value Theorem over the given interval. (b) Find c which satisfies the equation of the Mean Value Theorem: ), ( ' ) ( ) ( c f a b a f b f = - - on ] 2 , 2 1 [ .
Page 3 10/18/2011 5 [12 pts] . Let 1 3 ) ( 2 - + = x x x x f (Note that 2 2 ) 1 ( 3 2 ) ( ' - - - = x x x x f and 3 ) 1 ( 8 ) ( ' ' - = x x f ) (a) Find the intervals where f is increasing or decreasing. (b) Find the intervals where f is concave up or concave down.

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Unformatted text preview: (c) Find all local extrema (types and values of x and the function). (d) Find the equations of all asymptotes (vertical and oblique asymptotes). 6. Use Newton’s Method to approximate 3 . (a) [8 pts] Construct a function ) ( x f such that 3 is a root of ) ( = x f . Suppose 1 = x then use Newton’s method to construct 1 x and 2 x . 、 Page 4 10/18/2011 (b)[bonus 4 pts] Complete the sketch including labels (x0, x1 and x2) to graphically illustrate Newton’s Method and the determination of 1 x and 2 x . 7 [10 pts] . A rectangular box with volume 36 cubic centimeters is to be built with a square base and top. The material used for the base costs \$5 per square centimeter while the material used for the side panels and top costs \$3 per square centimeter. Find the minimum cost to build such a box....
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## This note was uploaded on 10/17/2011 for the course MTH 133 taught by Professor Staff during the Fall '08 term at Michigan State University.

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MTH132-Test3 - (c Find all local extrema(types and values...

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