101-2004&2005-2-M10-March2005(1)

101-2004&2005-2-M10-March2005(1) - jump or...

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Kuwait University Dept. of Math. Compo Sci. Math 101 First Exam Date: Duration: March 30, 2005 75 minutes Calculators, mobile phones, pagers and all other mobile communication equipment are not allowed Answer the following questions: 1. Evaluate the following limit, if it exists: (a) lim (x - 2)2 cot2 (x - 2) . x->2 (b) lim (x - 1) 2 cos ( 1 ). x->I x-I 2. Find the vertical and horizontal asymptotes, if any, for the graph of f (x) = VX2 + 4 x+4 3. Classify the discontinuities of (2 pts.) (2 pts.) (4 pts.) f (x) = as removable,
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Unformatted text preview: jump or infinite. x2 + 3x + 2 x+2 x+1 x2-1 , if x < 0, , if x > O. (5 pts.) 4. Use the'definition of the derivative to find 1'(2), where f (x) = V x3 + 1. 5. (a) State the intermediate Value Theorem. (4 pts:) (1 pts.) (b) Let f be continuous on (0,1) and 0 < f(x) < 1 for all x . Show that there is a number c in (0,1] with f(c) = c. (3 pts.) 6. Find l' (x), where x2 sin x f (x) = 1 + cos x . (4 pts.)...
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