Calculus Packet 7 Answer Key

Key Packet #7 30. (2008B BC2) For time t >= 0 hours, let r(t) = 120(1 - e ^ (-10r ^ 2)) represent the speed, in kilometers per hour, at which a car travels along a straight road. The number of liters of gasoline used by the car to travel x kilometers is modeled by g(x) = 0.05x(1 - e ^ ((- x) / 2)) Areas D 31. The area of the region enclosed by the curve y = 1/(x - 1) the x-axis, and the lines x = 3 and x 4 even (a) How many kilometers does the car travel during the first 2 hours? (b) Find the rate of change with respect to time of the number of liters of gasoline used by the car when t = 2 hours. Indicate units of measure. (c) How many liters of gasoline have been used by the car when it reaches a speed of 80 kilometers per hour? Area btwn curd Day 4: (31-41) no calc cross section Lou 6: 48-44 roc volume ✓ Day G: (45-59) odd Arcling/Sur face are Doy 7: (6192 G4 G571) REVIEW A) 5/36 calc C) ln(4/3) D) ln(3/2) E) In6 34 D 32. If 0 <= k < pi/2 and the area under the curve y = cos x from x = k to x = pi/2 is 0.1, then k = D) 1.120 E) 0.436 SK 4S3 dx= 33. The area of the region between the graph of y = 4x ^ 3 + 2 and the x-axis from x = 1tox = 2i D Sinx Sinx E)-9 Sx+a) belaw Lin A) 1.471 nocak B) 1.414 C) 1.277 cosx=1 A) 36 B) 23 C) 20 D) 17 Sing-sk=1 A 34. The area of the region in the first quadrant enclosed by the graph of y = x(1 - x) and the x-axis is sink. calc 1-\$ ink = 0.1 C) 2/3 D) 5/6 x(1 - x) = 0 E) 1 no calc A 35. The area of the region enclosed by the graphs of y = x ^ 2 and y = x - is A 1/6 calc B) 1/3 E) 1 of y = 1 + ln(cos^4 x) the x-axis, and the lines and B36. Let R be the region enclosed by the graph of x = 2/3 The closest integer approximation of the area of R is x = - 2/3 A) 0 B) 1 C) 2 D) 3 E) 4 33 1/3 1/2 ln(2/3) 5/6 oint - 7 3 1 + Ln(cos^4 x) * dx = 0.92 [[4x ^ 4], [4]] ^ 2 = (16 + 4) - (1 + 2) \\ 120-3-(17) matrix sum 0 X * (1 - x) = (x = 1)/0 x = 0x = 1 x(x - 1) = 0 K=\ overline a ^ - 1 , overline a (x ^ (2n))/2 - x/3 S_{0}(x) - x ^ 21 = 0.57 cole A 37. The area of the region in the first quadrant that is enclosed by the graphs of y = x ^ 3 + 8 and y = x + 8 1/4 B) 1/2 C) 3/4 D) 1 E) 65/4 \ Irhersectz x ^ 3 + 8 = x + 8 x(x ^ 2 - 1) = 0 x = plus/minus 1 C calc 38. The area of the region enclosed by the graphs of y = x and y = x ^ 2 - 3x + 3is S(x + 8) +(x^ 3 + overline 8 ) integrate - x ^ 2 + x = 0.25 dx from 0 to 1 A) 2/3 B) 1 C) D) 2 E) 14/3 3 x = x ^ 2 - 3x + 3 0 = x ^ 2 - 4x + 3 (x - 3)(x - 1) x = 3/1 * x = 1 5x + (x + 3x + 3) 3/5 - x ^ 2 + 4x - 3 = =1+ overline 3cos[4/n] p = f(x) no calc y = (g(a))' 39. The area of the shaded region in the figure above is represented by which of the following integrals? A) integrate (|f(x)| - |g(x)|) dx from a to x B) integrate f(x) dx from b to e - integrate g(x) dx from a to e C) integrate (g(x) - f(x)) dx from a to c (D) (f(x) - g(x)) * dx E) integrate (g(x) - f(x)) dx from a to h + integrate (f(x) - g(x)) dx from b to x -100 B no calc 40. Which of the following represents the area area of the shaded region in the figure above? A) int c ^ d f (y) * dy D) (b - a)[f(b) - f(a)] B) (d - f(x)) * dx C) f' * (b) - f' * (a) E) (d - c)[f(b) - f(a)]