# day2 - 1.65 10.404 1.70 10.665 1.75 10.932 1.80 11.203 1.85...

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Exam 2, Day 2, M175-001, Fall 2009 Name: 8. (10 pts.) Suppose that for a function f ( x ) we know the following: (a) | f ′′ | < 10 on the interval 0 x 2. (b) | f (4) | < 14 on the interval 0 x 2. (c) f ( x ) has the values as shown in the table at right. Compute i 2 0 f ( x ) dx with error no worse than 10 2 . Show work that proves your computation is su±ciently accurate. x f ( x ) 0.00 6.065 0.05 6.069 0.10 6.080 0.15 6.099 0.20 6.126 0.25 6.160 0.30 6.202 0.35 6.252 0.40 6.309 0.45 6.375 0.50 6.448 0.55 6.529 0.60 6.619 0.65 6.716 0.70 6.822 0.75 6.936 0.80 7.058 0.85 7.189 0.90 7.329 0.95 7.476 1.00 7.633 1.05 7.797 1.10 7.971 1.15 8.153 1.20 8.343 1.25 8.541 1.30 8.748 1.35 8.963 1.40 9.185 1.45 9.415 1.50 9.652 1.55 9.897 1.60 10.147

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Unformatted text preview: 1.65 10.404 1.70 10.665 1.75 10.932 1.80 11.203 1.85 11.477 1.90 11.754 1.95 12.033 2.00 12.313 1 9. (10 pts.) Consider the graph of y = 1 /x on the domain 1 ≤ x < ∞ . If this curve is revolved about the x-axis as shown below it forms an inFnitely long object. (a) Set up, but do not evaluate, an improper integral for the volume of this object. (b) Set up, but do not evaluate, an improper integral for the surface area of this object. Is the volume Fnite or inFnite? Is the surface are Fnite or inFnite? Convince me! y x 2...
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day2 - 1.65 10.404 1.70 10.665 1.75 10.932 1.80 11.203 1.85...

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