exam3 - recorded in the following table: t (s) 5 10 15 20 a...

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Exam 3 M170-003 Fall, 2006 Name: (1 pt.) Show all your work. 1. (10 pts.) Find the exact intervals on which f ( x ) = x 4 - x 3 - 3 x 2 is concave up and on which it is concave down. (NOTE: It is not necessary to fnd inc/dec or to graph f .) 1
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2. (10 pts.) Suppose that g ( x ) = sin 2 x + cos x , restricted to the domain 0 x 2 π . (a) Find the exact locations of all critical points in the domain. (b) Sketch a graph of g in which all increase and decrease intervals are perfectly visible. Label your axes. Don’t worry about concavity. Graph paper is provided below. 2
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3. (10 pts.) A box with a square end and unspecifed width is shown at right. Use diFerential approxi- mation to fnd the percentage change in its volume x changes by 3%. Show all your work. w x x 4. (10 pts.) ²ind lim x 0 x cos 3 x e 2 x - 1 3
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5. (15 pts.) The acceleration of a falling object (in m/s 2 ) is measured every 5 seconds and
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Unformatted text preview: recorded in the following table: t (s) 5 10 15 20 a (m/s 2 )-10-5-2-1 (a) Graph the acceleration data on the graph paper provided below. Be sure to label your graph properly. (b) Assuming initial velocity of v (0) = 0 m/s, compute v (20). (c) Shade an area in your graph that exactly matches your computation. 4 6. (15 pts) The graph of a function f is shown at right. The curved portion of f is a per-fect quarter-circle with radius 3. Assume g ( x ) = i x 4 f ( t ) dt f(t) 2 2 4 6 t (a) Compute g (6) (b) Compute g (1) (c) Compute g ( x ), where x is a Fxed location somewhere between-1 and 1. 5 7. (10 pts.) Compute i 2-2 (3 x 2 + x-3 + 6 cos x ) dx Use any methods (except asking your calculator). Be sure to show all your work. 6...
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exam3 - recorded in the following table: t (s) 5 10 15 20 a...

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