# Math Help - Limit

1. ## Limit

OK I am getting a different answer then the book.
Find the limit
x------>4
square root(x-3) - 1 / x-4
X-3 is the only part in the fraction that is square rooted.
I know you can bring it down and be lefted with
1/square (x-3) which gives you lim X=1 back the books says its one half so im doing something wrong .

2. Originally Posted by Nightasylum
OK I am getting a different answer then the book.
Find the limit
x------>4
square root(x-3) - 1 / x-4
X-3 is the only part in the fraction that is square rooted.
I know you can bring it down and be lefted with
1/square (x-3) which gives you lim X=1 back the books says its one half so im doing something wrong .
$\lim_{x\to4}\frac{\sqrt{x-3}-1}{x-4}=\lim_{x\to4}\frac{\sqrt{x-3}-1}{x-4}\cdot\frac{\sqrt{x-3}+1}{\sqrt{x-3}+1}$ $=\lim_{x\to4}\frac{x-3-1}{\left(x-4\right)\left(\sqrt{x-3}+1\right)}=\lim_{x\to4}\frac{1}{\sqrt{x-3}+1}$

I'm sure you can take it from here...

3. Ok so you acually rationalize the whole numerator? I was just doing the square root part.
Also can you help with
X---->-5
x^3+125/x+5

4. Originally Posted by Nightasylum
Ok so you acually rationalize the whole numerator? I was just doing the square root part.
Also can you help with
X---->-5
x^3+125/x+5
You will need to use the formula for factoring the sum of two cubes:

$a^3+b^3=(a+b)(a^2-ab+b^2)$

5. (x+5)(x^2-5x+5^2)/(x+5) = x^2-5x+5^2 = 75
I think I did that right I need to remember that formula thanks alot.

6. Originally Posted by Nightasylum
(x+5)(x^2-5x+5^2)/(x+5) = x^2-5x+5^2 = 75
I think I did that right I need to remember that formula thanks alot.

$\lim_{x\to-5}\frac{x^3+125}{x+5}=75$