101-2000&2001-2-F10-May2001 - Kuwait University...

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Kuwait University Dept of Math Comp Sci Math 101 Final Examination May 27, 2001 Duration: 2 hours (b) Answer the following questions. Calculators, Phones and Pagers are not allowed. Eeach question is worth 4 points 1. Ev~luate each of the following limits, if it exists. (a) lim 3/ 1 - 8x3 x-.co \ X (x2 + 1) 1. sin 2x - 2 sin x 1m x--.o x sin x 2. Let f (x) = 2 + .y x2 - 1. (a) Show that the graph of f has a vertical tangent at the point (1,2). (b) Does the graph of f have a cusp at the point (-1,2)? 3. Let y = .y2t2 + t - 9 and t = cot 2x + csc2 2x - 4. Find dy dx n at x = S. { cosx 4. Let f(x) = 1- x3 , if x < 0, , if x) O. Use the definition of the derivative to find l' (0). 5. Sand is falling into a conical pile at a r.ate of? m3 /sec. Th~ height of the cOl}eis always ~ the radius of its base. Find the rate of change of the radius of the pile when it contains 48nm3 of sand. 6. Evaluate the following integrals. " "2
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101-2000&amp;2001-2-F10-May2001 - Kuwait University...

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