Answers and Explanations 229
Answers
201–300
283.
1
2 x
Using the derivative definition with f x
x
( ) =
and with f x h
x h
+
(
)= + gives you
the following:
lim
lim
lim
h
h
h
x h
x
h
x h
x
x h
x
h x h
x
x h x
h x h
→
→
→
+ −
=
+ −
(
) + +
(
)
+ +
(
)
=
+ −
+ +
0
0
0
x x
h
h x h
x
x h
x
x
x
x
h
h
(
)
=
+ +
(
)
=
+ +
=
+ +
=
→
→
lim
lim
0
0
1
1
0
1
2
284.
−
−
5
2 2 5x
Using the derivative definition with f x
x
( ) =
−
2 5 and with
f x h
x h
x
h
+
(
)= −
+
(
)= − −
2 5
2 5
5 gives you the following:
lim
lim
h
h
x
h
x
h
x
h
x
h
x
h
x
x
h
→
→
−
−
−
−
=
−
−
−
−
−
−
+
−
−
−
0
0
2 5
5
2 5
2 5
5
2 5
2 5
5
2 5
2 5
5 + +
−






=
−
−
(
)− −
(
)
−
−
+
−
(
)
=
−
→
→
2 5
2 5
5
2 5
2 5
5
2 5
0
0
x
x
h
x
h
x
h
x
h
h
lim
lim
5 5
2 5
5
2 5
5
2 5
5
2 5
5
2 5
0
2 5
0
h
h
x
h
x
x
h
x
x
x
h
−
−
+
−
(
)
=
−
−
−
+
−
(
)
=
−
−
− +
−
(
)
=
→
lim
− −
−
5
2 2 5x