Part II: The Answers
228
Answers
201–300
281.
3x
2
– 2x
Using the derivative definition with f
 
(x) = x
3
– x
2
and with
f x h
x h
x h
x
x h
xh h
x
xh h
+
(
)= +
(
) − +
(
)
=
+
+
+ −
+
+
(
)
3
2
3
2
2
3
2
2
3
3
2
gives you the following:
lim
lim
h
h
x
x h
xh h
x
xh h
x
x
h
x h
xh h
→
→
+
+
+ −
−
− −
−
(
)
=
+
+
0
3
2
2
3
2
2
3
2
0
2
2
3
3
2
3
3
3 3
2
0
2
2
0
2
2
2
3
3
2
3
3
2
−
−
=
+
+ −
− )
(
=
+
+ −
−
→
→
xh h
h
h x
xh h
x h
h
x
xh h
x h
h
h
lim
lim (
)
(
=
+ + −
−
=
−
3
0 0 2
0
3
2
2
2
x
x
x
x
282.
6x + 4
Using the derivative definition with f
 
(x) = 3x
2
+ 4x and with
f x h
x h
x h
x
xh h
x
h
x
xh h
x
h
+
(
)=
+
(
) +
+
(
)
=
+
+
(
) + +
=
+
+
+
+
3
4
3
2
4
4
3
6
3
4
4
2
2
2
2
2
gives you the following:
lim
lim
lim
h
h
h
x
xh h
x
h
x
x
h
xh h
h
h
→
→
→
+
+
+
+ −
+
(
)
=
+
+
=
0
2
2
2
0
2
0
3
6
3
4
4
3
4
6
3
4
h h x
h
h
x
h
x
x
h
6
3 4
6
3 4
6
3 0 4
6
4
0
+ +
(
)
=
+ +
(
)
=
+
+
=
+
→
lim
( )