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## Main Question or Discussion Point

Prove by definition the statement

lim x->4 √x = 2

This is what I've done:

Given ε>0

|(√x)-2| = |√x-2|< ε if |x-4|< ε^2

I choose δ = ε^2

0<|x-4|< ε^2

=> |x-2|< √ε^2 = ε

Hence lim x->4 √x = 2

So, what do you think? Did I do the process correctly?

lim x->4 √x = 2

This is what I've done:

Given ε>0

|(√x)-2| = |√x-2|< ε if |x-4|< ε^2

I choose δ = ε^2

0<|x-4|< ε^2

=> |x-2|< √ε^2 = ε

Hence lim x->4 √x = 2

So, what do you think? Did I do the process correctly?

Last edited: