Answers and Explanations 231
Answers
201–300
287.
−
+
(
)
2
5
2
2
x
x
Using the derivative definition with f x
x
( ) =
+
1
5
2
and with
f x h
x h
x
xh h
+
(
)= +
(
) +
=
+
+ +
1
5
1
2
5
2
2
2
gives you the following:
lim
lim
h
h
x
xh h
x
h
x
x
xh h
x
x
→
→
+
+ +
−
+
=
+
(
) − + + +
(
)
+
0
2
2
2
0
2
2
2
2
1
2
5
1
5
1
5
2
5
2 h h h
x
h
xh h
h x
xh h
x
h
h
+ +
(
) +
(
)
=
−
−
+
+ +
(
) +
(
)
=
→
→
2
2
0
2
2
2
2
0
5
5
1
2
2
5
5
lim
lim
h h
x h
h x
xh h
x
x h
x
xh h
x
h
− −
(
)
+
+ +
(
) +
(
)
=
− −
+
+ +
(
) +
→
2
2
5
5
2
2
5
5
2
2
2
0
2
2
2
lim
( (
)
=
−
+ + +
(
) +
(
)
=
−
+
(
)
2
0 0 5
5
2
5
2
2
2
2
x
x
x
x
x
288.
7
4
2
x +
(
)
Using the derivative definition with f x
x
x
( ) =
+
+
2 1
4
and with f x h
x h
x h
(
)
(
)
+ =
+ +
+ +
2
1
4
gives
you the following:
lim
lim
h
h
x
h
x h
x
x
h
x
h
x
x
x
→
→
+ +
+ +
−
+
+
=
+ +
(
) +
(
)− +
(
) +
0
0
2
2 1
4
2
1
4
1
2
2 1
4
2
1
h h
x
x h
h
h
h x
x h
x
x h
h
h
+
(
)
+
(
) + +
(
)
=
+
(
) + +
(
)
=
+
(
) +
→
→
4
4
4
1
7
4
4
7
4
0
0
lim
lim
+ +
(
)
=
+
(
) + +
(
)
=
+
(
)
4
7
4
0 4
7
4
2
x
x
x