101-2008&2009-3-M10-July2009

101-2008&2009-3-M10-July2009 - Kuwait University...

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Kuwait University Math 101 Date: July 18, 2009 Calculators, cellular phones and all other mobile communication equipments are not allowed Answer the following questions: 1. Use the deFnition of the limit to show that lim x →- 2 (1 - 4 x ) = 9 (3 pts.) 2. Evaluate the following limits, if they exist: (a) lim x 1 x + 8 - 3 x 2 + 8 x - 9 (3 pts.) (b) lim x →∞ 1 x 2 sin ( x - 1) (3 pts.) 3. ±ind the vertical and horizontal asymptotes, if any, for the graph of f ( x ) = x 3 x 2 + 1 x 2 - 6 x + 8 . (4 pts.) 4. ±ind the x -coordinates of the points at which the function f is discontinuous, where f ( x ) = | x - 2 | ( x - 3) x 2 - 4 , if x < 3 , tan 2 ( x - 3) x - 3 , if x > 3 . Classify the types of discontinuity of f as removable, jump, or inFnite. (4 pts.) 5. (a) State the Intermediate Value Theorem. (1pts.) (b) Let g ( x ) = x 2 + f ( x ) , where f is a function with continuous derivative
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This note was uploaded on 02/23/2010 for the course CHEMISTRY 0420101 taught by Professor Dep during the Spring '10 term at Kuwait University.

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101-2008&amp;2009-3-M10-July2009 - Kuwait University...

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