Page 72 - Calculus Workbook For Dummies

56 Part II: Limits and Continuity

2
4. Pull the 16x out of the square root — it becomes –4x.
It becomes negative 4x because x is negative when x" 3- , and because you’ve got to pull out
a positive, you pull out –4x because when x is negative, –4x is positive. Got it?
3 x
= lim
x " - 3 3
4 x - - 4 xh 1 -
^
16 x
3 x
= lim
x " - 3 3
x 1 +
4 d 1 - n
16 x
5. Cancel and plug in.
3
= lim
x " - 3 3
4 1 + 1 - n
d
16 x
3
= J N
K
4 1 + 1 - 3 O
K 16 - h
3 O
^
L P
3
=
4 1 + 1 - 0j
`
3
= Piece o’ cake.
8
*v lim c 3 x 2 - 3 x 2 m = 6
x " - 3 x - 1 x + 1
2
1. Subtract the fractions using the LCD of (x – 1)(x + 1) = x – 1.
2 2
x x -
x x + h
3 ^ 1 - 3 ^ 1h
lim
2
x " 3 x - 1
2. Simplify.
2
3
3
3 x + 3 x - 3 x + 3 x 2
lim 2
x " 3 x - 1
6 x 2
lim 2
x " 3 x - 1
2
3. Your answer is the quotient of the coefficients of x in the numerator and the denominator
(see Case 2 in the “Into the Great Beyond” section).
= 6
Note that had you plugged in 3 in the original problem, you would have
33 2 33 2
3 - 1 - 3 + 1
= 3 - 3
= 0 ?
It may seem strange, but infinity minus infinity does not equal 0.