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Sum2010Exam1 - NAME MAC 2233 EXAM 1 PART 1 SHORT ANSWER 1(3...

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NAME: MAC 2233 EXAM 1 MAY 27, 2010 PART 1: SHORT ANSWER 1. (3 points) Give the definition of a function. 2. (3 points) Let f be a function. Give the three conditions f must satisfy to be continuous at x = a .
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3. (2 points) Let f be a function. Write the limit definition of f 0 ( a ), the derivative of f at x = a . 4. (4 points) State the intermediate value theorem.
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PART 2: PROBLEMS (Show All of Your Work) 1. (5 points) Find the equation of the circle with center (1 , 4) that passes through (3 , 3). 2. (5 points) Find the equation of the line that passes through (1 , 2) and is perpendicular to the line 3 x - 2 y = 1. Write your answer in slope-intercept form.
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3. Let f ( x ) = 2 x 2 - 3 and g ( x ) = x. (a) (3 points) Find and simplify ( f g )( x ). ( f g )( x ) = (b) (3 points) Give the domain of ( f g )( x ) in interval notation. Domain
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4. (4 points) A rectangular box is to have a square base and an open top. The volume of the box is to be 50 m 3 . The material for the base costs $3 per square meter and the material for the sides costs $2 per square meter. Find a function whose input x is the length of one side of the base and whose output C ( x ) is the cost of constructing the box.
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