Question

lim as x --> 1 ((sq rt of x) -1)/(x-1)

Answer 1

use conjugates

Answer 2

\[ \lim_{x\rightarrow 1} \frac{\sqrt{x}-1}{x-1} = \lim_{x\rightarrow 1} \frac{(\sqrt{x}-1)(\sqrt{x}+1)}{(x-1)(\sqrt{x}+1)} \]

Answer 3

\[ = \lim_{x\rightarrow 1} \frac{x-1}{(x-1)(\sqrt{x}+1)} = \lim_{x\rightarrow 1} \frac{1}{\sqrt{x}+1} = \frac{1}{2} \]

Answer 4

the answer is -1

Answer 5

Nope, thats wrong.

Answer 6

The answer is 1/2, check if you copied the problem correctly.

Answer 7

The answer is definitely 1/2. I prefer the way YTheManifold has done it, because it is very clear. But if we use a theorem and calculate it using L'Hopital's Rule, we would arrive at
\[\lim_{x \rightarrow 1} \ (1/(2\sqrt{x})) / 1 = 1/2\]