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Mathematics
Mathematics
Problem
What condition on a function
f
f
f
at the point
L
L
L
guarantees that
lim
x
→
a
f
(
g
(
x
)
)
=
f
(
lim
x
→
a
g
(
x
)
)
\displaystyle \lim_{x\to a} f\bigl(g(x)\bigr)=f\!\left(\lim_{x\to a} g(x)\right)
x
→
a
lim
f
(
g
(
x
)
)
=
f
(
x
→
a
lim
g
(
x
)
)
whenever
lim
x
→
a
g
(
x
)
=
L
\displaystyle \lim_{x\to a} g(x)=L
x
→
a
lim
g
(
x
)
=
L
?
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