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lecture prob1s11

# lecture prob1s11 - Calculus I(Nonengineering Spring 2011...

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Calculus I (Nonengineering), Spring 2011 Some Review Problems, Lectures 1 { 9 This problem set is not meant to be comprehensive. It gives more practice on some of the key concepts of the lectures. It will not be collected or graded, but you can ask your TA or lecturer for help, or ask at the Broward Teaching Center. The answers are given at the end of the problem set. 1. Find the domain of f ( x ) = r x 2 + 3 x ¡ 10 x ¡ 1 2. Sketch the graph of y = x 2 ¡ 5 x + 6 j x ¡ 3 j 3. Sketch the graph of f ( x ) = x 2 + 3 if x 1 4 ¡ x if x > 1 4. Sketch the graphs of f ( x ) = 4 ¡ x 2 and g ( x ) = 4 x ¡ x 3 x . Find lim x ! 0 f ( x ) and lim x ! 0 g ( x ). 5. Solve the equation 2 sin 2 x ¡ 2 p 2 sin x + 1 = 0 for 0 x < 2 . 6. If sin fi = 1 3 , tan fl = ¡ p 8 3 , and fi , fl are second quadrant angles, flnd the value of cos( fi + fl ). 7. Solve the inequality cot x < ¡ tan x for 0 x < 2 . 8. Sketch the graph of f ( x ) = 2 ¡ ( x +1) + 1. Find its inverse and graph the inverse on the same axes.

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