101-2008&2009-1-M10-November2008

101-2008&2009-1-M10-November2008 - Kuwait...

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Kuwait University Math 101 Date: November 17, 2008 Calculators, mobile phones, pagers and all other mobile communication equipments are not allowed Answer the following questions: 1. Evaluate the following limits, if they exist (a) lim x 0 x 1 - 1 + 3 x (2 pts.) (b) lim x 0 x + sin x 3 x - tan (2 x ) (2 pts.) 2. Find the x -coordinates of the points at which the function f is discontinuous, where f ( x ) = 2 x + 1 , if x < 0 , x 2 - x - 2 x 2 - 3 x + 2 , if x 0 . Classify the types of discontinuity of f as removable, jump, or in±nite. (4 pts.) 3. Find the vertical and horizontal asymptotes, if any, for the graph of f ( x ) = | x | ( x - 1) x 2 + x . (4 pts.) 4. (a) State the Intermediate Value Theorem. (b) Let f be continuous on [0 , 1] such that f (0) = a and f (1) = b, where a > 0 and b < 1 . Show that the equation f ( x ) = x has at least one root in (0 , 1) . (4 pts.)
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101-2008&amp;amp;2009-1-M10-November2008 - Kuwait...

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