2B-Final-Sample3.pdf - Math 2B Sample Final 3 Turn off your...

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Math 2B: Sample Final 3 • Turn off your cell phone and do not check it during the exam. • No calculators or other forms of assistance allowed. • This exam consists of 12 questions for 100 total points. Points per question are in brackets. • Read the directions for each problem carefully and answer all parts of each problem. • Unless instructed otherwise, show all work for full credit. • Define any notation used and label any sketches/graphs. 1. For the function drawn, estimate the area under the curve using a Riemann sum with four subintervals and midpoints. Sketch the Riemann sum by drawing rectangles on the picture. (5) 0 1 2 3 4 5 f ( x ) 0 1 2 3 4 5 6 7 8 x
2 2. Evaluate the following integrals (a) Z sin θ cos 2 θ d θ (3) (b) Z x - 7 ( x + 1 )( x - 3 ) d x (8)
3 3. Compute the average value f av of the function f ( x ) = x cos x on the interval [ 0, π 2 ] . (7) 4. A particle has velocity v ( t ) = 2 t - 5 ft/s at time t seconds. (a) Compute the displacement of the particle over the time inter- val t = 0 to t = 3. - 2 0 2 (4) - 4 v 1 2 3 t
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