101-2001&2002-2-F10-May2002

101-2001&2002-2-F10-May2002 - fav = x5. Find I (x)...

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Kuwait University Dept. of Math. Compo Sci. Math 101 Final Exam Date: Duration: May 26,2002 Two Hours Calculators, Mobile Phones and Pagers are not allowed AnSwer the following questions: 1. Evaluate the following limits, if exist: 3x~ - 27 (a) lim 1 3 x-+27 X3- e2 (b) ~~ 1- cosB ..•. (3 pts.) (3 pts.) 2. State The Intermediate Value Theorem. Prove that the graphs of f(x) = x5 + 2x4 - x3 + 2x - 1 and g(x) = 3x2 - 2x + 1, intersect. 3. Find the minimum value of S = gx + 8y2, where X(y2 + 1) = 2 and x =1= o. 4. Evaluate the following integrals: (4 pts.) (4 pts.) (a) J ~=x=2+=1== dx \j(x3 + 3x + 7)4 (4 pts.) 3 (b) J (y'g - x2 + x2 sin3 x + x) dx -3 (4 pts.) 5. Let x > 1, and suppose that the average value of a function f on the interval [1 x], is
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Unformatted text preview: fav = x5. Find I (x) . (4 pts.) 6. If I(x) = Hx2 + 2)~, find the arc length of the graph of I from x = a to x = )3. (4 pts.) 7. Find the area of the region bounded by the graphs of the equations y y = x + 2. and (4 pts.) 8. Let R be the region bounded by the graphs of the equations y = x2 + 4, 2x + Y = 2, x = a and x = 1. (a) Find the volume of the resulting solid if R is revolved about the line y = 5. (4 pts.) (b) Set up an integral that can be used to find the volume of the resulting solid if R is revolved about the line x = 2. (2 pts.)...
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This note was uploaded on 02/23/2010 for the course CHEMISTRY 0420101 taught by Professor Dep during the Spring '10 term at Kuwait University.

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