101-2000&2001-1-M10-October2000 - Math. 101 Date...

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Kuwait University f2-~~) Math. 101 Date Sci. First Exam. Duration October 19th, 2000 75 minutes. I Calculators, Mobile Telephones and Pagers are not allowed. Ans;wer all the following questions. Show your work. 1. Find the following limits, if they exist: a) lim x3 + 8 (3 pts.) ./X2 +x (3 pts.) X-t-CO 2x + 1 c) lim ./1 + sinx - 1 (3 pts.) tanx lim (x - 1)2 sin (_1_) (3 pts.) 2. Find the vertical and horizontal asymptotes, if any, of the graph of the function 3. Let k be a real number and f(x) ~ { Ixl j (x) = 2x - 3 ./x - k + 1-1 x-k if x> k if x < k . (3 pts.) Find all values ;of k so that j is continuous on (-co, co) . 4. Classify the discontinuities of j as removable, jump, or infinite, where j(x) = Ix - 11 (x - 2) 5. a) State the Intermediate Value Theorem. (3 pts.) (3 pts.) (1 pt.) b) Use the intermediate value theorem to show that the graphs of the equations y = x3 and y = x + 1 intersect. (3 pts.) Good Luck
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Kuwait University Dept. l\1ath.101
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101-2000&amp;amp;2001-1-M10-October2000 - Math. 101 Date...

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