Finite Limit at Infinity

ϵ

lim

x∞

f(x) = L

●

ϵ = 1.52565

M =

10

The function

f(x)

has a finite limit,

L

, as

x∞

. This means that for any

ϵ>0

, there is a number

M

such that

x>M

implies

|f(x)-L|<ϵ

. Adjust ϵ using the slider and then adjust the value of

M

to in such a way that, to the right of the

M

vertical, the graph lies between

L-ϵ

and

L+ϵ

. The function shown is

f(x)=4

-

x

5



sin(5x)+3

.