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e103k

# e103k - MAC 2311 Exam I Key July 8 2003 Prof S Hudson...

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MAC 2311 July 8, 2003 Exam I Key Prof. S. Hudson 1) [25pt] Short answer problems: a) Find the area of the sector below; it’s the part of the circle of radius 2 between θ = π/ 6 and θ = π/ 3. Answer: The angle in between is θ = π/ 6, so we have 1/12 of the whole circle. The area is πr 2 / 12 = π/ 3. b) Find all values of θ (in radians) that satisfy the equation cos( θ ) = - 1 2 Answer: These can point into the second or third quadrant, so there are two groups of answers; either θ = 3 π/ 4 + 2 or θ = 5 π/ 4 + 2 , where n is an integer. c) Solve x 2 - 4 x + 3 < 0. Answer: The parabola crosses the x-axis where 0 = ( x - 3)( x - 1), where x = 3 or x = 1. It is negative in between, where 1 < x < 3. d) Find the slope-intercept form of the line perpendicular to y = 5 x + 9 that has y -intercept 6. Answer: The perpendicular slope is m = - 1 / 5, so y = - x/ 5 + 6. e) Sketch a graph of f ( x ) = | x - 2 | + 1. Is f continuous? Answer: Draw a ”V” with a vertex at (2,1). It is continuous. 2) [10pt] Find the rate of change of the area A of a circle with respect to its circumference C .

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e103k - MAC 2311 Exam I Key July 8 2003 Prof S Hudson...

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