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101-2008&amp;2009-3-M20-August2009

# 101-2008&amp;2009-3-M20-August2009 - Kuwait University...

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Kuwait University Math 101 Date: August 1, 2009 Calculators, cellular phones and all other mobile communication equipments are not allowed Answer the following questions: 1. Use diFerentials to approximate 3 28 . (3 pts.) 2. ±ind an equation of the normal line to the curve sec ( x 2 y ) + r x 2 + y - x = 3 at x = 0 . (4 pts.) 3. A snow ball is melting in such a way that its surface area is decreasing at a rate of 1 cm 2 /min. ±ind the rate of change of its volume when the radius of the ball is 2 cm. (4 pts.) 4. (a) State Rolle’s Theorem. (1 pt.) (b) Use Rolle’s Theorem to show that for all a R , the equation 3 x 2 + sin x = a has at most one solution. (3 pts.) 5. Let f ( x ) = 4 - x ( x - 2) 2 and given that f p ( x ) = x - 6 ( x - 2) 3 and f pp ( x ) = 2 (8 - x ) ( x - 2) 4 . (a) ±ind the vertical and horizontal asymptotes for the graph of f, if any. (b) ±ind the intervals on which

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101-2008&amp;2009-3-M20-August2009 - Kuwait University...

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