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

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