Review for beginning of Math 242
This document covers some topics that you should have learned in Math 241
or whatever your equivalent course was.
If
x
= 3, evaluate
x
2
,

x
2
, 2
x
2
, and

2
x
2
.
If
x
=

3, evaluate
x
2
,

x
2
, 2
x
2
, and

2
x
2
.
Expand and simplify:
(
a
+
b
)(
x

y
+
z
) =
(
a
+
b
)(
a

b
) =
(
a
+
b
)(
a
2

ab
+
b
2
) =
(
a
+
√
b
)(
a

√
b
) =
2

√
3
2 +
√
3
·
2

√
3
2

√
3
=
(
√
x
2
+
x

x
)
·
√
x
2
+
x
+
x
√
x
2
+
x
+
x
=
Be very aware that
√
a
+
b
is
VERY DIFFERENT
from
√
a
+
√
b
(
a
+
b
)
2
is
VERY DIFFERENT
from
a
2
+
b
2
sin(
a
+
b
) is
VERY DIFFERENT
from sin
a
+ sin
b
‘n
(
a
+
b
) is
VERY DIFFERENT
from
‘n a
+
‘n b
Play around with this to convince yourself! Try some “nice” numbers, like
a
= 1 and
b
= 1. (For the sine function, examples of “nice” numbers might
be
a
=
π/
2 and
b
=
π/
2.)
1
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Solve the inequalities. In other words, for each inequality, find all values of
x
that make the inequality true.
x
2
<
9
x
2
>
9

x

3

<
2

x

3

>
2
Sketch the graphs of each of the following.
y
=
x
2
x
2
+
y
2
= 4
x
2
+
y
2
= 2
y
=
x
2
/
3
x
=
y
2
/
3
Where does
y
= 1 +
x
intersect
y
= 1 +
x
2
?
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 Spring '08
 wang
 Math, Trigonometry, lim, Inverse function, Inverse trigonometric functions

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