MHB Using the epsilon and delta definition to prove limit

[cbarker1]

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]

I'm pretty sure the square root function would succumb to http://mathhelpboards.com/math-notes-49/method-proving-some-non-linear-limits-4149.html of proving nonlinear limits.

 

[Krizalid1]

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.