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Mathematics
Mathematics
Problem
Which of the following limit expressions is equal to
f
′
(
a
)
f'(a)
f
′
(
a
)
for a differentiable function
f
f
f
at
x
=
a
x=a
x
=
a
? a)
lim
h
→
0
f
(
a
+
h
)
−
f
(
a
)
a
\displaystyle \lim_{h\to 0}\frac{f(a+h)-f(a)}{a}
h
→
0
lim
a
f
(
a
+
h
)
−
f
(
a
)
b)
lim
x
→
a
f
(
x
)
−
f
(
a
)
x
\displaystyle \lim_{x\to a}\frac{f(x)-f(a)}{x}
x
→
a
lim
x
f
(
x
)
−
f
(
a
)
c)
lim
Δ
x
→
0
f
(
a
+
Δ
x
)
−
f
(
a
)
Δ
x
\displaystyle \lim_{\Delta x\to 0}\frac{f(a+\Delta x)-f(a)}{\Delta x}
Δ
x
→
0
lim
Δ
x
f
(
a
+
Δ
x
)
−
f
(
a
)
d)
lim
x
→
a
f
(
a
)
−
f
(
x
)
x
−
a
\displaystyle \lim_{x\to a}\frac{f(a)-f(x)}{x-a}
x
→
a
lim
x
−
a
f
(
a
)
−
f
(
x
)
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