Infinite Limit at a Finite Point

M

lim

xc

1

2

(x-c)

= ∞

●

M = 45.9199

δ

1

=

0.147571

δ

2

=

0.147571

automatically calculate δ values

In words, the definition of

lim

xc

f(x)=∞

is that no matter how large

M

is, you can find an interval of width

δ

1

+

δ

2

around

c

(perhaps with

δ

1

and

δ

2

very small), so that

f(x)

will be larger than

M

as long as

x

is in that interval. This Demonstration computes the largest

δ

1

and

δ

2

for a given

M

. You can adjust

M

using the slider. The values for

δ

1

and

δ

2

may be found automatically or manually by dragging your mouse.