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Mathematics
Mathematics
Problem
The limit
lim
h
→
0
(
5
+
h
)
3
−
125
h
\displaystyle \lim_{h\to0}\frac{(5+h)^3-125}{h}
h
→
0
lim
h
(
5
+
h
)
3
−
125
represents a) the slope of the normal to
y
=
x
3
y=x^3
y
=
x
3
at
x
=
5
x=5
x
=
5
b) the slope of the tangent to
y
=
x
3
y=x^3
y
=
x
3
at
x
=
5
x=5
x
=
5
c) the average rate of change of
y
=
x
3
y=x^3
y
=
x
3
from
x
=
5
x=5
x
=
5
to
x
=
5
+
h
x=5+h
x
=
5
+
h
d) the slope of the tangent to
y
=
x
3
y=x^3
y
=
x
3
at
x
=
6
x=6
x
=
6
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