quiz2solutions - MAC1147: Quiz #2 09/08/2009 In the...

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Unformatted text preview: MAC1147: Quiz #2 09/08/2009 In the top-right corner of a clean sheet of paper, write your name, UFID, and section number. Please use a pen with blue or black ink. When you are nished, FOLD your paper in half lengthwise and write your name on the back. 1. Simplify 2x2 − 9x + 4 and nd its domain. 12 + x − x2 2x2 − 9x + 4 (2x − 1)(x − 4) (2x − 1) =− =− 12 + x − x2 (x + 3)(x − 4) (x + 3) Here the domain is simply x = −3; x = 4. In interval notation: (−∞, −3) ∪ (−3, 4) ∪ (4, ∞). 2. Solve: x4 − 5x2 + 6 = 0. (Hint: Use a substitution) Let u = x2 . Then the equation becomes u2 − 5u + 6 = 0, which can be solved as follows: (u − 3)(u − 2) = 0 u = 3; u = 2 x2 = 3; x2 = 2 √ √ x = ± 3; x = ± 2 3. Solve the inequality: −3 2 + x ≤ −6 3 x Dividing both sides by −3 gives |2 + | ≥ 2 (don't forget that the 3 inequality ips when we multiply or divide by a negative!). From here 1 x x the problem splits into two separate inequalities: 2+ ≥ 2 and 2+ ≤ 3 3 −2, which are easily solved to obtain x ≥ 0 and x ≤ −12, respectively. 2 ...
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quiz2solutions - MAC1147: Quiz #2 09/08/2009 In the...

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