Another limit question: (1 - x^(1/2)) / (1 - x) as x -> 1

[hank]

Here's the problem...

Find the limit as x->1 of (1 - x^(1/2)) / (1 - x)

I attempted it by trying to multiply by the conjugate, but that doesn't work.

Can anyone give me a hint?

 

[galactus]

Yes, it'll work. Multiply top and bottom by the conjugate of the numerator:

\(\displaystyle \L\\\frac{1-\sqrt{x}}{1-x}\cdot\frac{1+\sqrt{x}}{1+\sqrt{x}}\\=\frac{1-x}{(1-x)(1+\sqrt{x})}\)

Now, cancel what will cancel. See the limit?.