# limit of (sqrt(3x+6)-3)/(x-1) | x->1

• Jun 9th 2010, 07:32 AM
py592
limit of (sqrt(3x+6)-3)/(x-1) | x->1
Hi guy,

I would need help with a math problem in which one I must find the limit value of (sqrt(3x+6)-3)/(x-1) when x->1 wich is 0/0

Basically, what we have to do is find a way to remove that (x-1) under the division. The best I have done is (sqrt(3) * sqrt(x+2) - 3) / (x-1)

After that, I'm blocked
• Jun 9th 2010, 08:00 AM
skeeter
Quote:

Originally Posted by py592
Hi guy,

I would need help with a math problem in which one I must find the limit value of (sqrt(3x+6)-3)/(x-1) when x->1 wich is 0/0

Basically, what we have to do is find a way to remove that (x-1) under the division. The best I have done is (sqrt(3) * sqrt(x+2) - 3) / (x-1)

After that, I'm blocked

$\displaystyle \lim_{x\to1} \frac{\sqrt{3x+6} - 3}{x-1} \cdot \frac{\sqrt{3x+6}+3}{\sqrt{3x+6}+3}$

$\displaystyle \lim_{x\to1} \frac{3x+6 - 9}{(x-1)\sqrt{3x+6}+3}$

$\displaystyle \lim_{x\to1} \frac{3(x-1)}{(x-1)\sqrt{3x+6}+3}$

$\displaystyle \lim_{x\to1} \frac{3}{\sqrt{3x+6}+3} = \frac{1}{2}$
• Jun 9th 2010, 08:03 AM
py592
Oh ! Thank you. I totally forgot that trick
• Jun 9th 2010, 11:06 AM
p0oint
Another approach.

Divide the numerator and denominator by |x|.