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101-2002&amp;2003-2-M10-April2003

# 101-2002&amp;2003-2-M10-April2003 - Kuwait University...

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Kuwait University Dept. of Math. Camp. Sci. Math 101 First Exam Date: Duration: April 19, 2003 75 minutes Calculators, mobile phones, pagers and all other mobile communication equipments are not allowed Answer the following questions: 1. Evaluate the following limits, if exist: (a) lim .fi- 1 :z:~l x2 - 1 . (b) lim sinx + x3 sin 1 x_o x x 2. Find the vertical and horizontal asymptotes, if any, of Ixl I(x) = x2 _ x' 3. Classify the discontinuities of (3 pts.) (3 pts.) (5 pts.) [(x) ~ { as removable, jump or infinite. sin[1T(x + 1)] (x + 1)2 if, x> 0, if, x S; 0, (5 pts.) 4. (a) State the Intermediate Value Theorem. (1 pt.) (b) Show that x3 - x +1 J(x) = x2 + 1 has a horizontal tangent in [0,1]. (2 pts.) (u - 1)3 3 dy 5. (a) Ify= -- andu=ij2-3t-t2,find-att=2. u + 1 dt (3 pts.) (b) Find the point at which the graph of J(x) = 5(x + 1)2/5 + 2(x + 2)3/2 has a ~sp. (3 pts.) v;T,l- (Good Luck)

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2. Hm (IXII) Hm f(x) = lim 2-x =o=:>!y=olisH.Aforj. z-tCOX
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101-2002&amp;2003-2-M10-April2003 - Kuwait University...

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