101-2005&2006-3-M10-June2006 - (3 Points) b) Find...

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Kuwait University Math. Compo SeL Dept. Math 101 First Exam June 28, 2006 Time: 90 min. Calculators and Mobile Phones are not allowed. 1. Evaluate each of the following limits, if it exists: x-I a) lim ~ f3-= x-rl V 2x - v,) - x sinx b) lim ~+ ·xm2 X-rO V xv -r 2. Use the E, () definition of limit to show that: lim(5-2x) = 1. x-r2 3. Let f(x) = (x2 - 2x + l)lxl (x2-1)x . (3 Points) (3 Points) (3 Points) a) Find all points of dicontinuity of f and classify each discontinuity as removable, infinite, or a jump.
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Unformatted text preview: (3 Points) b) Find the vertical and horizontal asymptotes for the graph of f, (if any). (3 Points) 4. Show that the equation x5 + 2x-5 = 0 has at least one real root. 5. Assume lim f (x) exists and . x-r-l x2 + x-2 f (x) x2 + 2x-1----<---<----x + 3-(x-1)2 -x + 3 . Find lim f(x). x-r-l 6. Let f(x) = (x2-1) sec(~) + tan(x3-1). Find f'(x) (3 Points) (4 Points) (3 Points)...
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