This print-out should have 23 questions. Multiple-choice questions may continue on the next column or page – find all choices before answering. 001 10.0 points

huffmeister (kmh4546) – HW14 – yu – (53675) 1 This print-out should have 23 questions. Multiple-choice questions may continue on the next column or page – find all choices before answering. 001 10.0 points Find the most general antiderivative, F, of the function f(x) = 9x 2 − 4x + 6 . 1. F(x) = 3x 3 + 2x 2 + 6x 2. F(x) = 9x 3 − 4x 2 + 6x + C 3. F(x) = 3x 3 − 2x 2 + 6x + C 4. F(x) = 3x 3 − 2x 2 + 6x 5. F(x) = 3x 3 + 2x 2 + 6x + C 002 10.0 points Find the value of f(−1) when f ′′(t) = 9t − 5 and f ′ (1) = 3, f(1) = 4 . 003 10.0 points Find f(x) when f ′ (x) = 8 cos x − 5 sin x and f(0) = 3. 1. f(x) = −8 sin x + 5 cos x−2 2. f(x) = 8 sin x + 5 cos x−2 3. f(x) = −8 cos x + 5 sin x + 11 4. f(x) = 8 cos x + 5 sin x−5 5. f(x) = 8 cos x + 5 sin x + 11 6. f(x) = 8 sin x + 5 cos x−5 004 10.0 points Find all functions g such that g ′ (x) = 5x 2 + 4x + 5 √ x . 1. g(x) = √ x 5x 2 + 4x + 5 + C 2. g(x) = 2√ x x 2 + 4 3 x − 5 + C 3. g(x) = 2√ x x 2 + 4 3 x + 5 + C 4. g(x) = 2√ x 5x 2 + 4x + 5 + C 5. g(x) = √ x x 2 + 4 3 x + 5 + C 6. g(x) = 2√ x 5x 2 + 4x − 5 + C 005 10.0 points Find the most general function f such that f ′′(x) = 16 cos(4x). 1. f(x) = − cos(4x) + Cx + D 2. f(x) = −4 sin(x) + Cx2 + D 3. f(x) = 4 sin(4x) + Cx + D 4. f(x) = −4 cos(4x) + Cx2 + D 5. f(x) = sin(x) + Cx + D 6. f(x) = cos(x) + Cx + D 006 10.0 poi huffmeister (kmh4546) – HW14 – yu – (53675) 2 If F = F(x) is the unique anti-derivative of f(x) = (4 − x) 2 + 1 (4 − x) 2 which satisfies F(0) = 0, find F(3). 1. F(3) = 43 2 2. F(3) = 89 4 3. F(3) = 22 4. F(3) = 85 4 5. F(3) = 87 4 007 10.0 points Find the unique anti-derivative F of f(x) = 2e 5x + 3e 2x + 4e −3x e 2x for which F(0) = 0. 1. F(x) = 2 3 e 3x + 3x − 4 5 e −5x + 2 15 2. F(x) = 2 3 e 3x − 3x + 4 5 e −3x − 2 15 3. F(x) = 2 5 e 5x − 3x + 2 3 e −3x − 2 5 4. F(x) = 2 3 e 3x + 3x − 2 3 e −3x 5. F(x) = 2 5 e 5x + 3x − 4 5 e −5x − 2 5 6. F(x) = 2 3 e 3x − 3x + 4 5 e −5x − 22 15 008 10.0 points Find the value of f(π) when f ′ (t) = 1 3 cos 1 3 t − 6 sin 2 3 t and f π 2 = 4. 1. f(π) = − 11 2 + 1 2 √ 3 2. f(π) = − 9 2 + 3 2 √ 3 3. f(π) = 9 2 − 3 2 √ 3 4. f(π) = − 11 2 + 3 2 √ 3 5. f(π) = 9 2 − 1 2 √ 3 6. f(π) = 11 2 − 1 2 √ 3 009 10.0 points Find f(x) on − π 2 , π 2 when f ′ (x) = 4 + 3 tan2 x and f(0) = 4. 1. f(x) = 7 − x − 3 sec x 2. f(x) = 4 + x + 3 tan2 x 3. f(x) = 4 − x − 3 tan x 4. f(x) = 1 + 4x + 3 sec x 5. f(x) = 1 + 4x + 3 sec2 x 6. f(x) = 4 + x + 3 tan x 010 10.0 points If the graph of f passes through the point (1, 2) and the slope of the tangent line at (x, f(x)) is 6x − 7, find the value of f(2). 1. f(2) = 4 2. f(2) = 6 huffmeister (kmh4546) – HW14 – yu – (53675) 3 3. f(2) = 5 4. f(2) = 3 5. f(2) = 7 011 10.0 points If the graph of f is which one of the following contains only graphs of anti-derivatives of f? 1. 2. 3. 4. 5. 6. 012 10.0 points Find the value of y(1) when dy dx = 6e −3x − 8x, y(0) = 1. 1. y(1) = −2e −3 − 1 2. y(1) = −2e −3 + 7 huffmeister (kmh4546) – HW14 – yu – (53675) 4 3. y(1) = 2e −3 − 1 4. y(1) = 2e −3 + 7 5. y(1) = 2e −3 − 7 6. y(1) = −2e −3 − 7 013 10.0 points A stone is dropped off a cliff and falls under gravity with a constant acceleration of −32 ft/sec2 . If it hits the ground with a speed of 160 ft/sec, determine the height of the cliff. 1. height = 400 ft 2. height = 408 ft 3. height = 412 ft 4. height = 396 ft 5. height = 404 ft 014 10.0 points To avoid an accident a car brakes with a constant deceleration of 6 ft/sec2 , producing skid marks measuring 300 ft before coming to a stop. How fast was the car traveling when the brakes were first applied? 1. speed = 64 ft/sec 2. speed = 56 ft/sec 3. speed = 62 ft/sec 4. speed = 58 ft/sec 5. speed = 60 ft/sec 015 10.0 points Rewrite the sum S = 2 + 4 + 6 + . . . + 16 using sigma notation. 1. S = X 2 k = 1 8 2. S = X 8 k = 1 2k 3. S = X 2 k = 1 8k 4. S = X 16 k = 1 k 5. S = X 16 k = 1 8 6. S = X 8 k = 1 2 016 10.0 points Rewrite the sum n 4+1 9 2o + n 8+2 9 2o +. . .+ n 32+8 9 2o using sigma notation. 1. X 8 i = 1 n i + 4i 9 2o 2. X 8 i = 1 n 4i + i 9 2o 3. X 9 i = 1 4 n i + i 9 2o 4. X 9 i = 1 n 4i + i 9 2o 5. X 9 i = 1 4 n i + 4i 9 2o 6. X 8 i = 1 4 n i + i 9 2o huffmeister (kmh4546) – HW14 – yu – (53675) 5 017 10.0 points Estimate the area under the graph of f(x) = 19 − x 2 on [0, 4] by dividing [0, 4] into four equal subintervals and using right endpoints as sample points. 1. area ≈ 45 2. area ≈ 44 3. area ≈ 48 4. area ≈ 46 5. area ≈ 47 018 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 1 2 3 4 5 4 8 12 16 20 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. 41 ft < distance < 66 ft 2. 45 ft < distance < 62 ft 3. 43 ft < distance < 62 ft 4. 45 ft < distance < 64 ft 5. 43 ft < distance < 64 ft 6. 45 ft < distance < 66 ft 7. 41 ft < distance < 64 ft 8. 41 ft < distance < 62 ft 9. 43 ft < distance < 66 ft 019 10.0 points Estimate the area, A, under the graph of f(x) = 4 x on [1, 5] by dividing [1, 5] into four equal subintervals and using right endpoints. 1. A ≈ 5 2. A ≈ 79 15 3. A ≈ 76 15 4. A ≈ 77 15 5. A ≈ 26 5 020 10.0 points The graph of a function f on the interval [0, 10] is shown in huffmeister (kmh4546) – HW14 – yu – (53675) 6 -1 0 1 2 3 4 5 6 7 8 9 10 2 4 6 8 10 2 4 6 8 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 ≈ 51 2. area ≈ 53 3. area ≈ 52 4. area ≈ 54 5. area ≈ 55 021 10.0 points Estimate the area under the graph of f(x) = sin x between x = 0 and x = π 4 using five approximating rectangles of equal widths and right endpoints. 1. area ≈ 0.308 2. area ≈ 0.328 3. area ≈ 0.368 4. area ≈ 0.388 5. area ≈ 0.348 022 10.0 points Find an expression for the area of the region under the graph of f(x) = x 5 on the interval [3, 5]. (Use right hand endpoints as sample points.) 1. area = lim n→∞ Xn i = 1 3 + 3i n 5 2 n 2. area = lim n→∞ Xn i = 1 3 + 2i n 5 2 n 3. area = lim n→∞ Xn i = 1 3 + 2i n 5 3 n 4. area = lim n→∞ Xn i = 1 3 + 5i n 5 2 n 5. area = lim n→∞ Xn i = 1 3 + 3i n 5 3 n 6. area = lim n→∞ Xn i = 1 3 + 5i n 5 3 n 023 10.0 points Decide which of the following regions has area = lim n→ ∞ Xn i = 1 π 2n tan iπ 2n without evaluating the limit. 1. n (x, y) : 0 ≤ y ≤ tan(3x), 0 ≤ x ≤ π 4 o 2. n (x, y) : 0 ≤ y ≤ tan(4x), 0 ≤ x ≤ π 4 o 3. n (x, y) : 0 ≤ y ≤ tan(2x), 0 ≤ x ≤ π 2 o 4. n (x, y) : 0 ≤ y ≤ tan(x), 0 ≤ x ≤ π 4 o 5. n (x, y) : 0 ≤ y ≤ tan(3x), 0 ≤ x ≤ π 2 o 6. n (x, y) : 0 ≤ y ≤ tan(x), 0 ≤ x ≤ π 2 o

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