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short1-1b - 64 77 88 97 104(a(10 pts What is the rate of...

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Exam 1, Part 1, Form B M170-010, Fall, 2011 Name: (1 pt.) Show all your work. There are no trig, log, or exponential derivatives today, so you may use any methods on any problem. 1. A object placed in ice water is cooling down. Its temperature, T , as a function of time, x , is shown in the graph below. Temperature is measured in C; time is measured in minutes. (a) (5 pts.) Find Δ T on [1 , 9]. Give correct units. (b) (5 pts.) Find Δ T Δ x on [1 , 9]. Give correct units. (c) (5 pts.) Sketch a secant line in the graph that corresponds to your answer to (b). 2. (10 pts.) Compute lim u x x - u x - u 1
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3. A population of rabbits is growing. Population as a function of time is shown in the table below. t (months) 0 2 4 6 8 10 12 P (rabbits) 32 49
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Unformatted text preview: 64 77 88 97 104 (a) (10 pts.) What is the rate of change of population at the instant t = 4 months? (b) (10 pts.) When is the rate of change approximately 5 rabbits/month? 4. (10 pts.) f ( x ) = 1 4-x 2 . Find the slope of the tangent line at x = 3. 5. (10 pts.) A ball thrown up in the air has a height of h ( t ) = 30 t-16 t 2 feet after t seconds. At the instant when velocity is 14 ft/s, how high is the ball? 6. (5 pts. ea.) For each of the following functions, compute f ′ ( x ). Assume that a and b are constants. Assume that g is an unknown function of x . (a) f ( x ) = bx 2 + x + 5 (b) f ( x ) = x ( a + bx ) 3 (c) f ( x ) = x-g 32 x 2 + 2 x 9 2...
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short1-1b - 64 77 88 97 104(a(10 pts What is the rate of...

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