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Unformatted text preview: x : dy dx cos y. (c) Compute the derivative of f ( x ) = x e x . 2. Compute the following limits. (a) lim x cosh x-1 x 2 (b) lim x 1 + 3 x x (c) lim x + 1 x + ln x 3. Let f ( x ) be the following function, dened for all positive real numbers: f ( x ) = 3 + ln x < x < 1 3 cos( x/ 2) 1 x 5 tan-1 x x > 5 . . If x is your answer to this question, then your score is f ( x ), rounded down to the nearest integer if necessary. If f ( x ) is negative you will get a score of zero. 4. Sand falls from a conveyor belt at a rate of 10 m 3 /min onto the top of a conical pile. The height of the pile is always equal to the diameter of the base. How fast is the height changing when the pile is 4 m high? 5. Sketch a graph of the function y = e-x 2 . 2...
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- Spring '10