Limits Q (Uni) (1 Viewer)

[mreditor16]

Hi,

I just wanted to confirm my answer for this Q (and if I'm wrong, explain how I'm wrong).

This is the Q



I got a) exists b) 3 c) not too sure

So some help please

 

[InteGrand]

Hi,

I just wanted to confirm my answer for this Q (and if I'm wrong, explain how I'm wrong).

This is the Q



I got a) exists b) 3 c) not too sure

So some help please

It exists, limit is 3, reason: by epsilon-delta definition of limit.

 

[mreditor16]

It exists, limit is 3, reason: by epsilon-delta definition of limit.

LOL that's my logic. but I'm not too sure about whether I need a better explanation. is that more than enough?

 

[InteGrand]

LOL that's my logic. but I'm not too sure about whether I need a better explanation. is that more than enough?

Not sure. You could say "we are given that, for any , whenever x is within units of 1, is within units of 3, hence by the ε-δ definition of the limit, the limit is 3".

 

[photastic]

|f(x) - 3| < ε , ε > 0

1 - ε/2 < x < 1+ ε/2 (This is what the brackets mean)
- ε/2 < x - 1 < ε/2
|x - 1| < ε/2
Take δ = ε/2 given ε > 0
Blah blah