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Unformatted text preview: MAC1147: Quiz #2
09/08/2009
In the topright 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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 Summer '08
 GERMAN
 Calculus, section number, Black Ink, clean sheet

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