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101-2003&2004-2-M10-March2004 - 1 as jump removable...

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Calculators, mobile phones, pagers and all other mobile communication equipment are NOT allowed Instructions: (i) Read each question carefully. (ii) Remember to show all work in order to receive full credit. 1. Evaluate the following limit, if it exists, (2 pts. each) March 31,2004 Exam Duration: 75 min. Math 101 1st Midterm Test Kuwait University Departement of Math and CS (a) I. 2x + 2tan3x Im----- x ...... o sin2x lim [3X+(X-3)4sin ~] x ...... 3 2. Find the vertical and horizontal asymptotes, if any, for (4 pts.) 1 (x) = 2x2-x 3. Let iZ'" Jx + 21 1 (x)- Classify the discontinuities of
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Unformatted text preview: 1 as jump, removable or infinite. 4. (a) State the intermediate value theorem. (b) Use the intermediate value theroem to show that the equation (5 pts) (1 pt.) x2 cos7fX + 3x-1 = has a real root. G pts.) 5. (a) Use the definition of the derivative to find I' (1), where (2 pts. each) 1 (x) ~ 1 (b) Find an equation of the normal line to the graph of f at x = 1. 6. Find l' (x), where (4 pts.) 1 (x) = secx Note that it is important that you try to solve ALL questions. Good Luck!...
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