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Unformatted text preview: Inequalities
Inequalities
Section 2.5 Interval Notation
Interval Let c and d be real numbers with c < d.
Let [c, d] denotes the set of all real numbers x
denotes
such that c < x < d. (c, d) denotes the set of all real numbers x
(c,
such that c < x < d. [c, d) denotes the set of all real numbers x
denotes
such that c < x < d. (c, d] denotes the set of all real numbers x
denotes
such that c < x < d. [ ] represents closed interval. ( ) represents open interval. Basic Principles for Solving
Inequalities
Inequalities 1.
2.
3. Performing any of the following operations
Performing
on an inequality produces an equivalent
inequality.
inequality.
Add or subtract the same quantity on both
Add
sides of the inequality.
sides
Multiply or divide both sides of the
Multiply
inequality by the same positive quantity.
positive
Multiply or divide both sides of the
Multiply
inequality by the same negative quantity
negative
and reverse the inequality sign.
and Solving Inequalities
Solving
1. Write the inequality in one of the following
Write
forms. f(x) > 0 f(x) > 0 f(x) < 0 f(x) < 0
f(x)
f(x)
f(x)
f(x)
2. Determine the zeros of f, exactly if
Determine
exactly
possible, approximately otherwise.
possible,
3. Determine the interval, or intervals, on the
Determine
xaxis where the graph of f is above (or
axis
below) the xaxis. Joke Time
Joke Why was the baby cookie
Why
sad?
sad? His mother was a wafer a
His
while.
while. Why couldn’t the elephant
Why
hide in the cherry tree?
hide He forgot to paint his toenails
He
red.
red. ...
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 Winter '11
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 Calculus, Real Numbers, Inequalities

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