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UFCalcSet1

# UFCalcSet1 - Exercises UF Calculus Set 1 1 Rewrite the...

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Exercises UF Calculus Set 1 1. Rewrite the expression without absolute value bars (let x be a real number): (a) | π - 5 | (b) | 2 x + 1 | (c) | 2 x - 1 | if x < 1 2 (d) write an expression for | 2 x | - x 2. Solve each equation for x : (a) 1 x + a = 2 x - 1 - 1 x - a , where a , b are constants (b) x + 2 x - 3 = 0 (c) 1 - 2 x x = 3 x (d) ( x 2 - 1) 1 / 2 - ( x 2 - 1) - 1 / 2 (2 - x 2 ) x 2 - 1 = 0 (be sure to write in simplest form first) 3. Solve each inequality for x : (a) x 3 - 5 x 4 x 2 (b) | 1 - 4 x | - 7 ≤ - 2 (c) -| 2 x + 3 | < - 4 (d) 2 x 3 (e) 3 x 2 + 1 x + 1 2 (f) (Challenge problem) - 2 1 x < 5 4. Verify that the triangle whose vertices are given by the points ( - 2 , 1) , (2 , 3) and (3 , 1) is a right triangle. Find its area. 5. Find all points with y -coordinate - 3 whose distance from the point ( - 2 , 1) is 5. 6. Write the equation (in slope-intercept form) of the line passing through the point (1 , - 3) which is parallel to the line 2 x + 3 y = 12 . 7. Find the equation of the perpendicular bisector of the line segment joining the points (1 , 3) and (5 , - 7) .

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