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209-1-sample

# 209-1-sample - r = 0 1(10 annually how many whole years it...

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DEPARTMENT OF MATHEMATICS AND STATISTICS MATH 209 First class test October 04, 2006 1. Find the limits [20pts] (a) lim x →- 2 (2 x 2 + 5 x - 2), (b) lim x 1 x 2 + x - 2 x - 1 . 2. Find the derivatives f 0 ( x ) of the following [40pts] (a) f ( x ) = 1 4 x - 4 + 2 x + 4 e 2 x , (b) f ( x ) = (6 x 2 + 4) 4 , (c) f ( x ) = x 2 - 4 x 2 +4 , (d) f ( x ) = ln( x + 2). 3. For f ( x ) = x 3 + 4 x - 2 calculate [20pts] (a) the slope of the tangent line at x = 2, (b) the equation of the tangent line at x = 2. 4. [10pts] If the interest is compounded continuously at the rate
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Unformatted text preview: r = 0 . 1 (10% annually), how many whole years it needs for the money to double? 5. [15pts] Market studies for a new processor model showed that the demand of it, depending on the price p , is x = 1 , 000 , 000-10 , 000 p . (a) Find marginal revenue at x = 400 , 000 (b) Find average revenue per unit at x = 400 , 000....
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