101-2004&2005-1-M10-October2004

101-2004&2005-1-M10-October2004 - Kuwait University...

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Kuwait University Math 101 Date: October 28, 2004 Dept. of Math. & Compo Sci. First Exam Duration: 75 minutes Calculators, mobile phones, pagers and all other mobile communication equipment are not allowed Answer the following questions: 1. Use the definition of the limit to show that: lim (7 - 2x) = -l. x->4 2. Evaluate the following limits, if they exist: (a) lim [(x - 1)2 sin ( 7r ) + 2] x->l x-I (b) lim 2x + sin 3x x->o x - tan 6x (3 pts.) (3 pts.) (3 pts.) 3. Find the x-coordinates of the points at which the function f is discontinuous, where f(x) = ~ x3 - 8 Classify the types of discontinuity of f as removable, jump, or infinite. 4. (a) State The Intermediate Value Theorem. (b) Show that f (x) = 3x4 + 6x3 + x2 + x + 1 , has a real root. 5. Use the definition of the derivative to find l' (3), where f (x) = Jx + 1. (4 pts.) (1 pt.) (2 pts.) (3 pts.) 2 6. Find the points on the graph of f(x) = _x_,at which the tangent line is horizontaL x+1 (3 pts.) 7. Find l' (x) , where f (x) = sin4 (5x3 + x + 2) - csc Jx2 + 1. (3 pts.)
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2 + 3lim sin3x 3x-+O 3x :!.
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