/sci/ - Science & Math

[Anonymous No.9949677]

How do I prove
$$\lim_{x\to 1} \frac{1}{x}$$
Using the epsilon-delta definition?

I tried delta equals epsilon times x, but I'm not sure if delta can depend on x. Could you help a brainlet?

[Anonymous No.9949683]

>>9949677
Fuck, let me get it right:

[math]\lim_{x\to 1} \frac{1}{x}[/math]

[Anonymous No.9949684]

>How do I prove
>$$\lim_{x\to 1} \frac{1}{x}$$
>Using the epsilon-delta definition?
You can't prove an expression.

[Anonymous No.9949689]

From [math]|\frac{1}{x} -1|<\epsilon [/math] I came to the conclusion that [math]|x-1|<x\epsilon[/math], but I dont know if I can assume delta to be that.

[Anonymous No.9949690]

>>9949684
Oh yea, i forgot to add "equals one", I'm sorry. Thank you for saying that.

[Anonymous No.9949692]

>>9949683
>>9949677
==LET ME GET IT ACTUALLY RIGHT THIS TIME!==

[math]\lim_{x\to 1} \frac{1}{x} = 1[/math]

[Anonymous No.9949696]

Is it ok to assume that [math]\delta = x\epsilon [\math]? If it isn't, how can I get the actual delta?

[Anonymous No.9949701]

>>9949696
[math]\delta = x \epsilon [\math]

[Anonymous No.9949715]

Well, I'm going to sleep. I plan to reply during the morning.

[Anonymous No.9950247]

>>9949683
let eps > 0
choose a delta such that
delta < eps/(1 + eps)
let x such that |x - 1| < delta
then, |1/x - 1/1| = |1 - x|/|x| < delta/|x| < delta/(1 - delta) < eps