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Areas using Riemann sums-problems-1

Areas using Riemann sums-problems-1 - handa(nh5757 –...

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Unformatted text preview: handa (nh5757) – Areas using Riemann sums – bormashenko – (54880) This print-out should have 11 questions. Multiple-choice questions may continue on the next column or page – ﬁnd all choices before answering. 1 42 3. S = k k=1 7 001 10.0 points Evaluate k=1 4 n=2 1. 6k 4. S = n+1 . n−1 42 5. S = 18 5 7 k=1 6 6. S = 2. 5 7 k=1 3. 20 3 004 4. 4 10.0 points Estimate the area under the graph of 5. None of these 002 f (x) = 4 sin x 10.0 points 15 (5 − 2k ). between x = 0 and x = π using ﬁve approx3 imating rectangles of equal widths and right endpoints. k=12 Evaluate the given sum. 1. area ≈ 2.375 1. −80 2. area ≈ 2.355 2. −84 3. area ≈ 2.415 3. None of these 4. area ≈ 2.395 4. −92 5. area ≈ 2.335 005 5. −88 003 10.0 points Rewrite the sum Rewrite the sum 4+ S = 6 + 12 + 18 + . . . + 42 using sigma notation. 1 9 2 + 8+ 6 7k i 9 2 4i + i=1 7 i 9 2 4i + 1. k=1 9 2. S = 6 k=1 2 9 using sigma notation. 6 1. S = 10.0 points 2. i=1 2 + . . . + 24+ 6 9 2 handa (nh5757) – Areas using Riemann sums – bormashenko – (54880) 9 4 i+ 3. i=1 9 4 i+ 4. i=1 6 5. i=1 4 i+ i=1 006 i 9 6. 52 ft < distance < 69 ft 2 7. 52 ft < distance < 65 ft 4i 9 4i i+ 9 6 6. i 9 2 2 8. 54 ft < distance < 65 ft 9. 50 ft < distance < 67 ft 2 007 10.0 points Estimate the area under the graph of 2 f (x) = 18 − x2 10.0 points Cyclist Joe brakes as he approaches a stop sign. His velocity graph over a 5 second period (in units of feet/sec) is shown in on [0, 4] by dividing [0, 4] into four equal subintervals and using right endpoints as sample points. 1. area ≈ 45 20 2. area ≈ 41 16 3. area ≈ 43 4. area ≈ 44 12 5. area ≈ 42 8 008 10.0 points Estimate the area, A, under the graph of 4 f ( x) = 1 2 3 4 5 Compute best possible upper and lower estimates for the distance he travels over this period by dividing [0, 5] into 5 equal subintervals and using endpoint sample points. 1. 50 ft < distance < 65 ft on [1, 5] by dividing [1, 5] into four equal subintervals and using right endpoints. 1. A ≈ 2. A ≈ 2. 50 ft < distance < 69 ft 3. A ≈ 3. 54 ft < distance < 67 ft 4. A ≈ 4. 54 ft < distance < 69 ft 5. A ≈ 5. 52 ft < distance < 67 ft 5 x 20 3 77 12 79 12 19 3 13 2 009 10.0 points handa (nh5757) – Areas using Riemann sums – bormashenko – (54880) Estimate the area, A, under the graph of n 4 f ( x) = x 1. on [1, 5] by dividing [1, 5] into four equal subintervals and using right endpoints. 2. i=1 n i=1 n 010 10.0 points 3. i=1 The graph of a function f on the interval [0, 10] is shown in n 4. i=1 9 8 7 6 5 4 3 2 1 n 5. 8 i=1 n 6 6. i=1 4 2 0 -1 2 4 6 8 10 Estimate the area under the graph of f by dividing [0, 10] into 10 equal subintervals and using right endpoints as sample points. 1. area ≈ 52 2. area ≈ 54 3. area ≈ 51 4. area ≈ 55 5. area ≈ 53 011 10.0 points Rewrite the sum 4 2 5+ n n 2 + 4 4 5+ n n +...+ using sigma notation. 2 4 2n 5+ n n 2 4 2i 5i + n n 4 2i 5+ n n 2i 4i 5+ n n 2 4i 5+ n n 2 2 2 2 2 4i 5i + n n 2 2i 4i 5+ n n 2 3 ...
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