This question was asked and answered earlier here.
Hi i need help on how to prove a limit does not exist using the epsilon-delta definition of the limits.
Its like lim x--> 5 1/x-5 does not exist
how do i go about proving that this limit does not exist? and what do you think is a good approach to proving limits using the definition?
Thank you,
Angelo
I'm not sure but I think you meant ...so suppose the limit exists and equals L, then:
(*)
On the other hand, the expression can be made as big (as negative big) as wanted by choosing x close enough to 5 from the right (from the left): , and this contradicts (*) above since there is bounded...
- If the proof is easier, by making x approach 5 from the left (from the right).
- Tonio
ouu thats right, sorry about that.
But the answer there was handled using one sided limits which I know is a very good way of proving it and it works. But my question is how do i go about proving this limit does not exist using the:
epsilon - delta definition?
∀ε > 0, ∃δ > 0 such that 0<|x-c|<δ ---> |f(x) - L| < ε