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[SOLVED] Using the epsilon and delta definition to prove limit

Cbarker1

Active member
Jan 8, 2013
241
Find the limit L. Then use the epsilon-delta definition to prove that the limit is L.

$\sqrt(x)$ as x approaches 9

I figure out the first part of the question. the Answer is three. Yet I have some difficulty to answer the second part of the question.


Thank you

Cbarker11
 

Ackbach

Indicium Physicus
Staff member
Jan 26, 2012
4,192
I'm pretty sure the square root function would succumb to this method of proving nonlinear limits.
 

Krizalid

Active member
Feb 9, 2012
118
Put $x=t^2,$ so $\displaystyle\lim_{x\to9}\sqrt x=\lim_{t\to3}t=3.$ Since the original limit is positive, we require that $|t|=t.$
So you can prove your result using the latter limit.