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practicefinalB[1]

practicefinalB[1] - Math 1550 Practice Final Fall 2007...

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Math 1550, Practice Final, Fall 2007 Problem 1. Pick TWO (2) of the following 4 problems. Find the first derivatives and their critical points. (10 min/20 pts ) (a) f ( x ) = 2 x 2 e 1 /x (b) f ( x ) = (2 x + 1) ln(2 x + 1) (c) f ( x ) = sin x 2 sin x + 3 3 (d) f ( x ) = x 2 + 4 x - 11 x + 5 Problem 2. Pick TWO (2) of the following 4 problems. Evaluate the integrals. [10mts, 20pts] (a) e x e e x cos( e e x ) dx (b) π/ 4 - π/ 4 cos x sin x sin 2 x + 2 dx (c) 10 - 10 2 + x (4 x 2 + 1) 3 dx (d) 6 x (3 x + 1) 2 dx Problem 3. Pick ONE (1) of the following two problems. (5 min/20 pts) (a) Discuss the function (even, odd, lim x →±∞ f ( x ), vertical asymptotes, intercepts, increasing, decreasing, maxima and minima, concave up, concave down, points of inflection, and finally a sketch of the graph). Show all work. f ( x ) = 1 - 2 x x 10 f ( x ) = 5 - 9 x 2 x 9 f ( x ) = 10(11 - 18 x ) x 12 . (b) Set up integrals (first using vertical slices and then with horizontal slices) for the volume of the solid obtained by rotating the region bounded by curves y = 2 x , x = 3, and y = 0 about the axis y = 6. Do not evaluate the integrals.
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