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Mapping a Convergent Sequence by a Continuous Function

slope
1.5
intercept
0.25
y
0
= f(
x
0
)
0.25
ϵ > 0
0.25
δ > 0
0.1
a
m
and f(
a
m
)
1
vertical andhorizontal lines
This Demonstration illustrates the following theorem: If
lim
n
a
n
=
x
0
and
f
is continuous at
x
0
, then
lim
n
f(
a
n
)=f(
x
0
)
.
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