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Calculus Review - Calculator 1. Let h(x) be the anti- derivative of g(x). If - 1

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Calculus Review - Calculator 2. The acceleration of a particle moving on a line is given by: If the particle starts from rest, what is the distance traveled from t=0 to t=3.61? - 2

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Calculus Review - Calculator 3. On each point (x, y) on a curve, the slope of the curve is If the curve contains the point (0,7), then which of the following is the equation of the curve? - 3

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Calculus Review - Calculator 4. The volume, V (cubic inches) of unmelted ice remaining from a melting ice cube after t seconds is given by How fast is the volume changing when t = 40 sec? - 4

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Calculus Review - Calculator 5. - T1 T2 2 -2 -1 1 5

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Calculus Review - Calculator 6. If the function f is defined as on the interval[-7,5], then g(x) has a local minimum at x = ? - -2 0 5 x + -1 - 4 + g(x) inc dec inc There is a local min at x = 4 6

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Calculus Review - Calculator 7. The normal line to the graph at x = 1 also intersects the graph at which one of the following values of x? A. -1.18 B. -1.11 C. -1.06 D. -0.98 E. -0.86 - 7

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Calculus Review - Calculator 8. Let R be the region in the first quadrant bounded above by y = 4x + 3 and below by Find the area of R - Bottom Find the point of intersection 8 Top

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Calculus Review - Calculator 9. A conical cup 8 inches across the top and 12 inches deep is leaking water at the rate of 2cu in /min A. At what rate is the water level dropping when the water is 6 in deep. - 9

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Calculus Review - Calculator 9. A conical cup 8 inches across the top and 12 inches deep is leaking water at the rate of 2cu in /min B. At what height is the water level dropping when the cup is half full? - 10

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Calculus Review - Calculator 10. Consider the differential equation and let y = f(x) be a solution. A. On the axis provided, sketch a slope field at the 20 indicated points. - 11 (x,y)0123 01111 1½½½½ 20000 3- ½ -½-½ 4

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Calculus Review - Calculator 10. Consider the differential equation and let y = f(x) be a solution. B. Find the general solution y = f(x) - 12

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Calculus Review - Calculator 10. Consider the differential equation and let y = f(x) be a solution. C. Find the particular solution to the differential equation with the initial condition f(2 ln 3) = 4 - 13

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Calculus Review - Calculator 11. Find the approximate volume generated by revolving the first quadrant area enclosed by y = 3x + 4, and the y-axis about the x-axis - Outer inner Find the points of intersection using your calculator: (.966, 6.90) Use the washer method 14

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Calculus Review - Calculator 12. A ball is thrown from the top of a 1200-ft building. The position function expressing the height h of the ball above the ground at any time t is given as Find the average velocity for the first 6 seconds of travel - 15

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Calculus Review - Calculator 13. For the ellipse what is the value of at the point in the third quadrant where x = -1 - 16

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Calculus Review - Calculator 14. A function f is defined on the interval [0,4] x [-2,5], and its derivative is A. Sketch f’ in the window [0,4] x[-2,5] Use your calculator to find the graph then do a rough sketch 17

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Calculus Review - Calculator 14. A function f is defined on the interval [0,4] x [-2,5], and its derivative is B. On what interval is f increasing? Justify your answer. f is increasing when f’(x) >0, this is true for all values between a and b Find where Using calculator A = 0.293 < x < 3.760 18

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Calculus Review - Calculator 14. A function f is defined on the interval [0,4] x [-2,5], and its derivative is C. At what value(s) of x does f have local maxima? Justify your answer. - - + - 0 a b 4 Since f decreases to the right of endpoint x = 0 f has a local maximum at x = 0. There is a local max at x = 3.760 because it changes from increase to decrease 19

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Calculus Review - Calculator 14. A function f is defined on the interval [0,4] x [-2,5], and its derivative is D. How many points of inflection does the graph of f have? Justify your answer. - 0 P Q R 4 inc dec inc dec f’(x) + - + - f”(x) cu cd cu cd f(x) Since the graph of f changes concavity at p, q, and r there are 3 points of inflection 20

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Calculus Review - Calculator 15. The rate of sales of a new software product is given by where S is measured in thousands of units sold per month and t is measured in months from the initial release of the product on January 1, 2007. A. This product initially sold at the rate of 2500 units per month, and the sales rate has doubled every three months. Find C and k - 21

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Calculus Review - Calculator 15. The rate of sales of a new software product is given by where S is measured in thousands of units sold per month and t is measured in months from the initial release of the product on January 1, 2007. B. Find the average rate of sales for the first year. - 22

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Calculus Review - Calculator 15. The rate of sales of a new software product is given by where S is measured in thousands of units sold per month and t is measured in months from the initial release of the product on January 1, 2007. C. Using the midpoint rule with three equal subdivisions, write an expression that approximates 3 equal subdivisions at 4, 5, 6, 7 With delta x = 1, midpoints will be at 4.5, 5.5, and 6.5 Midpoint Rule 23

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Calculus Review - Calculator 15. The rate of sales of a new software product is given by where S is measured in thousands of units sold per month and t is measured in months from the initial release of the product on January 1, 2007. D. Using correct units, explain the meaning of in terms of software sales. - Represents the number of units sold, in thousands, during May, June, July in 2007 24

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