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Mathematics
Mathematics
Problem
Identify the correct limit expression that represents
d
d
x
(
x
3
)
\dfrac{d}{dx}\bigl(x^{3}\bigr)
d
x
d
(
x
3
)
at a general point
x
x
x
. a)
lim
h
→
0
(
x
+
h
)
3
−
(
x
−
h
)
3
h
\displaystyle \lim_{h\to0}\frac{(x+h)^{3}-(x-h)^{3}}{h}
h
→
0
lim
h
(
x
+
h
)
3
−
(
x
−
h
)
3
b)
lim
h
→
0
(
x
−
h
)
3
−
x
3
h
\displaystyle \lim_{h\to0}\frac{(x-h)^{3}-x^{3}}{h}
h
→
0
lim
h
(
x
−
h
)
3
−
x
3
c)
lim
h
→
0
(
x
+
h
)
3
−
x
3
h
\displaystyle \lim_{h\to0}\frac{(x+h)^{3}-x^{3}}{h}
h
→
0
lim
h
(
x
+
h
)
3
−
x
3
d)
lim
h
→
0
(
x
+
h
)
3
−
x
3
h
2
\displaystyle \lim_{h\to0}\frac{(x+h)^{3}-x^{3}}{h^{2}}
h
→
0
lim
h
2
(
x
+
h
)
3
−
x
3
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