Calculus - Definition of the Limit - help

So the question is:

Use the definition of the limit to prove:
lim c = c
x→a

I've written, Given ε>0, δ=ε/0. If 0< 0< δ then IcI-c = Ic-cI = 0>0δ = 0(ε/0)=0

But it's supposed to =ε so what did I do wrong?

Thanks!

Reply 1

Smaug123

15

Original post by Airess3

So the question is:

Use the definition of the limit to prove:
lim c = c
x→a

I've written, Given ε>0, δ=ε/0. If 0< 0< δ then IcI-c = Ic-cI = 0>0δ = 0(ε/0)=0

But it's supposed to =ε so what did I do wrong?

Thanks!

You seem to have divided epsilon by zero? Also you have the line "if

0 < 0 < \delta

", a condition which is never satisfied because

0 \geq 0

.

Can you state the definition of "limit" for me first?

By the way, the pipe character | is much more comprehensible than I.

Reply 2

username970964

OP

14

Original post by Smaug123

You seem to have divided epsilon by zero? Also you have the line "if

0 < 0 < \delta

", a condition which is never satisfied because

0 \geq 0

.

Can you state the definition of "limit" for me first?

By the way, the pipe character | is much more comprehensible than I.

Let f be a function defined by an open interval, containing 'a', except possibly not at 'a' itself. We say, the "limit as x approaches a is L", and write: lim(f(x))=L.
x→a
If for every ε greater than 0, there is delta greater than 0, such that if 0 is lesser than |x-a| lesser than delta then |f(x) -L| lesser than epsilon.