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MAT285-2006Spring

MAT285-2006Spring - MAT 285 Final Exam Spring 2006 Name...

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---------- ----------- ----------- MAT 285 Final Exam Spring 2006 Instructor: Name: Student ID: I. Evaluate the following limits: 4 -x a. lim 4 3 2 x--+«> X - 7 x + 7 x + 9 , t2 - 3t + 2 b . I Im---- 1-41 t 2 - 1 , .[;-2 c. I Im-- X-44 X - 4 2. Use the definition of the derivative: f' (x) = lim f(x + h) - f(x) to calculate the h-4O h derivative of: f(x) = £
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3. The graph of f(x) is given below: -3 -3 a. Using the above graph, find the following limits (if a limit does not exist, then write DNE) lim f(x) x -; 1 + lim f(x) x -; -1 l i m f(x) x -; 1 lim f(x) x -; 2 b. At which of these points is f(x) continuous? (explain) -4, -2, 2, 4 c. At which of these points is f(x) differentiable? (explain) -4, -2, 2, 4
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4. Find the indicated derivatives: hex) = sin(3x + 2) -7x h'(x) = cos(3x + 2) p(x) = 7 sin(3x) p"(x) =
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5. The number of gallons of water in a tank t minutes after the tank has started to drain is Q(t) = 200(30 - t)2. a. How fast is the water running out at the end of 10 min? b. What is the average rate at which the water flows out during the first 10 min? 6. A rocket is rising VERTICALLY from its launching pad. An observer is positioned 1000 feet from the launching pad. Find the rate
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