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101-1999&amp;2000-3-F10-July2000

# 101-1999&amp;2000-3-F10-July2000 - Kuwait University...

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University Dept. of Math. Compo Sci. Math. 101 Final Exam. July 29, 2000 Duration: 2 hours Calculators and mobile phones are not allowed. Answer the following questions. Each question is worth 4 Points. 1. Find the following limit, if it exists 1. sin(x - 2) 1m 2 . x---*2 X - 4 2. Let f('~) ~ { x2 + 2x - 3 if x =I- ± 1, , x2 -1 4. Let 3. Show that the equation x7 + 5x + 3 = 0 has exactly one real root. {A + 2x, if x:::;; 1, f(x) = 2 - B x2 , if x > 1. Find the constants A and B so that f is differentiable at x = 1. 5. Find the equation of the normal line to the graph of the equation VX+y'Y=3 at the point where x = 1. 6. Find l' (x), if 7. Evaluate the following integrals: 7r/4 (a) J tan2 xdx, o tanx (b) f(x) = J 3t3dt. x3 1 (b) J x dx. y5 - x2 -1 8J Find the area of the region bounded by the graphs of the equations x + y2 = 4 and x = O. The region bounded by the graphs of the equations 2 d 2 y=x an x=y is revolved about the line y = -3. Find the volume of the resulting solid. 10. Find

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101-1999&amp;2000-3-F10-July2000 - Kuwait University...

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