WOLFRAM|DEMONSTRATIONS PROJECT

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
)
.