Part II: The Answers
232
Answers
201–300
lim
h
h
h
x
h
x
x
x
→
→
=
+ +
(
) +
(
)− +
(
) +
0
0
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
289.
x
x
x
2
2
6
1
3
+
−
+
(
)
Using the derivative definition with f x
x
x
( ) =
+
+
2
1
3
and with
f x h
x h
x h
x
xh h
x h
+
(
)=
+
(
) +
+ +
=
+
+ +
+ +
2
2
2
1
3
2
1
3
gives you the following:
lim
lim
h
h
x
xh h
x h
x
x
h
x
xh h
x
→
→
+
+ +
+ +
−
+
+
=
+
+ +
(
) +
(
)−
0
2
2
2
0
2
2
2
1
3
1
3
1
2
1
3
x x
x h
x h
x
h
hx
xh h x
h h
h x h
h
2
0
2
2
2
1
3
3
3
1
6
3
3
+
(
) + +
(
)
+ +
(
) +
(
)
=
+
+
+
−
+ +
→
lim
( (
) +
(
)
=
+
+
+
−
(
)
+ +
(
) +
(
)
=
+
+ + −
+
→
x
h x
x hx
h
h x h
x
x
x
x
h
3
6
3 1
3
3
6
0 0 1
0
2
2
lim
0 0 3
3
6
1
3
2
2
+
(
) +
(
)
=
+
−
+
(
)
x
x
x
x
290.
2
3 2
1
2 3
x +
(
)
Using the derivative definition with f x
x
( ) =
+
2 1
3
and with
f x h
x h
x
h
+
(
)=
+
(
)+ =
+ +
2
1
2
2 1
3
3
gives you
lim
lim
h
h
x
h
x
h
x
h
x
h
→
→
+ + −
+ =
+ +
(
) − +
(
)
0
3
3
0
1 3
1 3
2
2 1
2
1
2
2 1
2
1