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Chapter 5 Practice Exam

Chapter 5 Practice Exam - n and L n(5 points 3 State the...

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92.132 Calculus II Chapter 5 Practice Exam Name________________________________________________________ September 25, 2009 1. Estimate the area under the graph of f(x) = x 2 + 2 from x = 0 to x = 4 by computing R 4 and L 4 . (20 points, each part worth 2 points) (a) What is Δx? (b) List the partition points and their values. (c) List the sample points for R 4 and their values. (d) List the sample points for L 4 . and their values. (e) Write an expression for R 4 using sigma notation. (f) Write an expression for L 4 using sigma notation. (g) Write an expression for R 4 expanding the sigma notation in part (e). (h) Write an expression for L 4 expanding the sigma notation in part (f). (i) Complete the computation of R 4 by substituting appropriate numerical values in the expression in (g). (j) Complete the computation of L 4 by substituting appropriate numerical values in the expression in (h).

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2. (a) Write, in expanded form, an expression for an arbitrary Riemann sum. (5 points) (b) How does an arbitrary Riemann sum differ from the specific Riemann sums R
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Unformatted text preview: n and L n ? (5 points) 3. State the definition of a definite integral. (5 points) 4. Use the Midpoint Rule with n = 3 to approximate dx x ∫ 7 1 1 . (10 points) 5. Use the Evaluation Theorem (FTC2) to evaluate dx x x ) 4 2 1 ( 3 1 3 ∫-+ . (10 points) 6. If oil leaks from a tank at a rate of r(t) gallons per minute at time t, what does ∫ 120 ) ( dt t r represent? (5 points) 7. State The Fundamental Theorem of Calculus. (5 points) 8. The velocity function (in ft/sec) for a particle moving along a line is given by v(t) = t 2 – 4t + 3. During the interval 1 ≤ t ≤ 5, find (a) the displacement of the particle (5 points) (b) the total distance traveled by the particle (10 points) 9. (a) Find the average value of f(x) = x over [0, 4]. (5 points) (b) Find the c guaranteed by The Mean Value Theorem for Integrals. (5 points) 10. (a) Evaluate the indefinite integral dx ∫ + 2 2 ) 1 (x x . (5 points) (b) Evaluate the definite integral dx x x ) cos( 2 ∫ π . (5 points)...
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Chapter 5 Practice Exam - n and L n(5 points 3 State the...

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