Math 1351 013 Exam I C February 6 2004 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 16 pts Let P 4 2 and Q 3 2 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 D Find the equation of the line passing through P and Q Write the equation in standard form 2 8 pts Solve the equation 5 3 y 4 3 8pts Solve algebraically the system of equations 4 12 pts Let f x 3x 8 y 2 2 x 4y 6 x 1 2x 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 2 B2 f 1 5 12 pts Let f x 3 2 x A Find the inverse of f B Sketch the graphs of f and f 1 on same coordinate system 6 6pts 1 Find the exact value of tan cos 1 2 7 6pts Simplify sin cos 1 x B3 f 1 8 12pts 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 A1 f 1 B1 A2 f 1 A3 lim f x B2 lim f x B3 lim f x C2 lim f x C3 lim f x D2 lim f x D3 x 1 C1 x 1 D1 x 1 x 1 x 1 x 1 9 24 pts Algebraically evaluate each of the following limits A lim x 1 x2 2x 7 x2 x 1 6 x x2 x 3 3 x 2 C lim sin 22x x 0 x B lim f 2 lim f x x 2 lim f x x 2 lim f x x 2
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