Easy Limit

Calculus Level 1

What is the value of $\displaystyle\lim_{x\to1}\frac{\sqrt{x}-1}{\sqrt{x-1}} .$

1 solution

Parth Tandon
Jun 4, 2015

L-Hospital's rule..................:)

$\displaystyle\lim_{x\to1}\frac{\sqrt{x}-1}{\sqrt{x-1}}$

Now rationalize the numerator .

$\displaystyle\lim_{x\to1}\dfrac{x-1}{\sqrt{x-1}\cdot (\sqrt{x} + 1)} \\= \displaystyle\lim_{x\to1}\frac{\sqrt{x-1}}{\sqrt{x}+1}$

Now apply the limits and you are done .

A Former Brilliant Member - 6 years ago

Does L-hpital rule apply when x is not going to 0 or infinite?

Xi Huang - 6 years ago

It applies when the rational function has indeterminate form. It doesn't matter whether $x$ is tending to a specific value, or infinity.

Calvin Lin Staff - 6 years ago