Math 1351 011 Exam I D September 22 2006 Answer the problems on separate paper You do not need to rewrite the problem statements on your answer sheets Do your own work Show all relevant steps which lead to your solutions Attach this question sheet to the front of your answer sheets 1 12 pts Let P 3 2 and Q 2 4 be points in the plane A Plot P and Q on a Cartesian coordinate system B Find the distance between P and Q C Find the coordinates of the midpoint M of the line segment PQ 2 10 pts Solve A the equation 4 3 y 8 B the inequality x 2 4 x 0 3 4 pts Find the center and radius of the circle given by x 2 y 2 2 x 10 y 2 0 4 4 pts Find the equation of the line which passes through 2 3 and is parallel to the line given by 3 x 4 y 4 5 12 pts Let f x x x 1 A Find the domain of f B Compute the following functional values or state that the corresponding x value is not in the domain of f B1 f 1 6 6 pts Simplify tan cos 1 2 x 7 6 pts Solve the equation log 4 x log 4 x 15 2 B2 f 0 B3 f 2 8 15 pts Consider the function f defined by the graph to the right Find each of the following if they exist If they do not exist state so Also determine if the function is continuous at the given point If it is not continuous at the given point state so A1 B1 C1 D1 E1 f 1 A2 f 1 A3 lim f x B3 lim f x C3 f 2 lim f x B2 lim f x C2 lim f x D2 lim f x D3 lim f x Is f continuous at 1 E2 Is f continuous at 1 E3 Is f continuous at 2 x 1 x 1 x 1 x 1 x 1 x 1 lim f x x 2 lim f x x 2 x 2 9 24 pts Algebraically evaluate each of the following limits x 2 3x 2 A lim 2 x 1 x 2 x 2 x2 x 6 B lim 2 x 3 x 3 x 4x2 C lim 2 x 0 sin 2 x cos x 2x a x 1 10 8 pts Find the constant a so that f x 2 will be continuous at x 1 2ax 1 x 1
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