MTH132-Quiz5

# MTH132-Quiz5 - base and height that use the least amount of...

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Page 1 10/18/2011 Name (Print Clearly): Student Number: MTH132 Section 1 & 12, Quiz 5 March 27，2009 1 [3 pts each] . Find the limits. (a) 2 2 2 2 3 lim π + - + - -∞ x x x x (b) 4 / cos sin lim 4 / π π - - x x x x (c) θ θ θ cos 1 2 lim 2 0 - (d) [bonus 2pts] ) sin 1 1 ( lim 0 x x x - + 2. Suppose 1 3 ) ( 3 + - = x x x f . (a) [2 pts] . Find ) ( ' x f and ) ( ' ' x f .

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Page 2 10/18/2011 (b) [2 pts] . Find all critical points and inflection points. Use first derivative test to find local extreme values. (c) [1 pt] . Graph this function (plot all key points and sketch the curve). 3. A square-based open-top rectangular holding tank is to hold 500 cubic meters. Find the dimensions for the
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Unformatted text preview: base and height that use the least amount of material. (a) [2 pts]. What are the given information and target (objective) function? (b) [2 pts]. Use the given information to eliminate a variable to obtain a new target function and its domain. (c) [2 pt]. Minimize the new target function and find the dimensions for the base and height....
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