Answers and Explanations 193
Answers
101–200
To find the limit, substitute 3 for x:
lim
( )
x
x x
x
→
−
+ +
(
)
=
−
+ +
(
)
=
−
( )
= −
3
1
3
2
1
3 3 3
2 3
1
3 2 6
1
6 6
187.
12
Note that substituting the limiting value, 0, into the function
2
8
3
+
(
) −
h
h
gives you the
indeterminate form 0
0
.
Expand the numerator and simplify:
lim
lim
lim
li
h
h
h
h
h
h
h
h
h
h
h
h
h
→
→
→
+
(
) −
=
+
+
+ −
=
+
+
=
0
3
0
3
2
0
3
2
2
8
6
12
8 8
6
12
m m
lim
h
h
h h
h
h
h
h
→
→
+ +
(
)
=
+ +
(
)
0
2
0
2
6 12
6 12
To find the limit, substitute 0 for h:
lim
( )
h
h
h
→
+ +
(
) = + + =
0
2
2
6 12 0 6 0 12 12
188.
1
Note that substituting in the limiting value, 4, gives you the indeterminate form 0
0
.
Because x is approaching 4 from the right, you have x > 4 so that x
x
− =
−
4
4
(
).
Therefore, the limit becomes
lim
lim
lim
x
x
x
x
x
x
x
→
→
→
+
+
+
−
−
=
−
−
=
=
4
4
4
4
4
4
4
1
1