101-2005&amp;2006-3-M20-July2006

# 101-2005&amp;2006-3-M20-July2006 - if any d Sketch the...

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Kuwait University Math. Camp. Sci. Dept. Math 101 Second Exam July 17, 2006 Time: 90 min. Calculators and Mobile Phones are not allowed. 1. Use differentials to approximate: sin (29° ). (3 Points) 2. Find the equation of the normal line to the curve: tan(xy) + vx + y = 1 at x = O. (4 Points) 3. A plate in a shape of a disk is heated. If the area A of the plate (in cm2) after time t (in hours) is given by A = Jt2 + 3t + 6, find the rate at which the radius of the plate is changing after two hours. (4 Points) 4. a) State the Mean Value Theorem. (1 Point) b) Let f be a function such that f'Cx) < k, "Ix, with f(O) = 3 and f(3) = 6. Find all possible values of k for such function to exist. (3 Points) 3-x x-5 2(7-x) 5. Let f(x) = I ,\<)' and given that j'(x) = I ,\'1 and fl/(x) = .... a) Find the vertical and horizontal asymptotes for the graph of J, if any. b) Find the intervals on which the graph of f is increasing and the intervals on which the graph vf f is decreasing. Find the local extrema of f, if any. c) Find the intervals on which the graph of f is concave upward and the intervals on which the graph of f is concave downward. Find the points of inflection,

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101-2005&amp;2006-3-M20-July2006 - if any d Sketch the...

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