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Unformatted text preview: Polytechnic Institute of NYU MA 1424 Exam 3 Practice Fall 2008 Studying from past or sample exams is NOT recommended. If you do, it should be only AFTER you know how to do all of the homework and worksheet problems. These are additional practice problems designed to cover the material, but not necessarily specific to the exam. (1) (Worksheet 7) Using your knowledge of the behavior of rational and exponential functions, circle ALL of the integrals below that converge. (a) 1 1 1 + x dx (b) 1 1 + x dx (c) xe x 2 dx (d) 1 1 x (ln x ) 2 dx (e) 1 x 3 4 x 2 2 x + 1 x 5 + x 3 + 1 dx (f) 2 4 x 2 + 3 3 x 3 + x + 1 dx (g)  1 e 3 x dx (h) 8 2 1 ( x 3) 2 dx (i) 1 ( x 3) 2 / 3 (2) Decide if each integral converges or diverges. If the integral converges, find its value or give a bound on its value. (a) we w dw (b) 1 1 x 4 dx (c)  2 1 4 + z 2 dz (d) 1 x x + 1 dx (e) 1 (sin( x )) 3 / 2 dx 1 2 (3) (Worksheet 8) In each part, circle the correct choice. You need not show any work. Consider the following Figure: 4 h 5 l Figure 1 (a) Determine the Riemann sum that represents the area of the Figure. (i) 4 5 h (5 h ) h (ii) 4 5 (5 h ) h (iii) (5 h ) h (iv) 45 h h (v) 5 h (b) Use the definite integral to find the area of the region. (i) 20 (ii) 15 (iii) 10 (iv) 5 (v) 4 3 (4) (Worksheet 8) In each part, circle the correct choice. You need not show any work. Consider the following Figure: w y 4 Circle Figure 2 (a) Determine the Riemann sum that represents the area of the Figure. (i) 2 y 2 y (ii) 4 y 2 y (iii) 2 2 y 2 y (iv) 2 4 y 2 y (v) 2 (2 + y ) 2 y (b) Use the definite integral to find the area of the region. (i) 20 (ii) 16 (iii) 8 (iv) 4 (v) 2 4 (5) (Worksheet 8) Consider the region bounded by y = 9 ( x 1) 2 , y = 4 2 x and the xaxis, for 0 x 4. Hint: Sketch this region. (a) Find the area of this region. (b) Find the volume obtained by rotating this region around the xaxis....
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 Fall '09
 HarvanshManocha
 Calculus, Addition

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