Last Limit Q: lim (4 - x^1/2)/(16 - x) as x -> 16

[Aduial.Elen]

Here's another question my friend couldn't get (and neither could I). I feel like I'm clogging up this board and I do apologize.


THe limit as x approaches 16.

It's a fraction with numerator 4-x^1/2 and denominator 16-x

Many thanks!

 

[skeeter]

big hint ...

\(\displaystyle \L 16 - x = (4 - \sqrt{x})(4 + \sqrt{x})\)

 

[galactus]

Multiply by the conjugate of the numerator:

\(\displaystyle \L\\\lim_{x\to\16}\frac{4-\sqrt{x}}{16-x}\cdot\frac{4+\sqrt{x}}{4+\sqrt{x}}\)

Go ahead and do the algebra. The limit will appear. Post back with your answer.

 

[Aduial.Elen]

I get 1/8 as my answer. Thanks so much everyone!