MTH132-Test3 - = x x x f(a Find the intervals where f is...

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Page 1 10/18/2011 Name (Print Clearly): Student Number: MTH132 Section 5 & 18, Test 3 Nov 7, 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 limits of each of the following functions. (a) 1 1 lim 3 / 2 5 / 3 1 - - x x x (b) ) sin( sin lim 2 2 0 x x x (c) 2 / 3 2 2 3 3 2 lim x x x x x + - -
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Page 2 10/18/2011 2. [4 pts each] . Find indefinite integrals. (a) - + - dx x x ) 2 3 ( 2 3 / 1 (b) + dr r 2 ) 5 ( 1 (c) [4 pts bonus] - dt t t 2 sin 1 sin 3. [8 pts]. Solve initial value problem: 1 ) 0 ( ), cos( = = 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.
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Page 3 10/18/2011 (b) Find c which satisfies the equation of the Mean Value Theorem: ), ( ' ) ( ) ( c f a b a f b f = - - on ] 2 , 2 1 [ . 5 [12 pts] . Let 2 2 ) 3 ( ) ( - = x x x f (Note that 3 ) 3 ( 6 ) ( ' - - = x x x f and 4 ) 3 ( 18 12 )
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Unformatted text preview: '-+ = x 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. (c) Find all local extrema and inflection points. (d) Find the equations of all asymptotes. Page 4 10/18/2011 6 [10 pts] . A rectangular box with volume 18 cubic meters is to be built with a square base and NO top. The material used for the bottom panel costs $2 per square meter while the material used for the side panels costs $1.5 per square meter. Find the minimum cost to build such a box. 7. [10 pts]. Use Newton’s Method to approximate 15 . (a) Construct a function ) ( x f such that 15 is a root of ) ( = x f (b) Find an initial guess x of the solution then use Newton’s method to construct 1 x and 2 x ....
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