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Unformatted text preview: Kuwait University Math 101 Date: December 21, 2008 Dept. of Math. & Comp. Sci. Second Exam Duration: 90 minutes Calculators, mobile phones, pagers and all other mobile communication equipments are not allowed Answer the following questions: 1. Find dy dx and d 2 y dx 2 , at x = 0 , where 2 y + sin ( xy ) = 1 . (4 pts.) 2. The volume of a cube is increasing at a rate of 30 cm 3 / sec . How fast is the total surface area of the cube increasing when the length of each edge of the cube is 10 cm long? (4 pts.) 3. Use di¡erentials to approximate 3 √ 1 . 03 . (3 pts.) 4. Find the absolute extrema, if any, of f ( x ) = sin x + cos x on b π 2 , 3 π 2 B . (3 pts.) 5. Use Rolle’s Theorem to show that the equation x 7 + 4 x 3 + x- 2 = 0 cannot have two di¡erent roots. (3 pts.) 6. Let f ( x ) = ( x + 3) 2 x . (a) Find the intervals on which f is increasing and the intervals on which f is de- creasing. Find the local extrema of f, if any....
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