MAT284-2006Spring

# MAT284-2006Spring - M ay 8 2 006 P rofessor H siang M AT 2...

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May 8, 2006 Professor Hsiang MAT 284 Final Exam version 1 Signature _ SU ID # _ **************** Show your work. No work-no credit! 2 3 10 12 4 5 6 7 8 9 8 9 11 Total 125 1

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1. A person wishes to invest \$300,000.00 in two enterprise so that the total income per year will be \$21,600.00. On enterprise pays 6% annually; the other has more risk and pays 7.5% annually. How much must be invested in each? [10 points] 2. If f(x) = 2x 2 and g(x) = 3x 2 + x, find the following expressions. Simplify your answers. [(2.5 points for each part) x (4 parts) = 10 points total] (a) (J - g)(x) = (b) (J 9 ) (x) = (c) = (i) (x) 3
(d) U 0 g) (:r) = 3. Let y = 3x - 5 be an equation of a line land (-3, 2) be a point P. Find an equation of a line passing through point P and perpendicular to line l: What are the slope and y-intercept of this line? [10 points] 4. Find the limits. [(3 points for each part) x (4 parts) = 12 points total] (a) lim (t-2) = t->(-3) t + 5 4

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(b) lim (x 3 - 3x 2 - 2x + 1) = x--+( -1) 2 (c) lim x - x - 2) = ~ x--+2 ( x - 2 3X2 - 1 ) (d) lim - x--+(-oo) ( 5x 2 + 4x - 3 - 5. Differentiate the following functions.
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MAT284-2006Spring - M ay 8 2 006 P rofessor H siang M AT 2...

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