# evalute this limit

• Aug 24th 2010, 04:34 AM
banku12
evalute this limit
$\displaystyle \lim_{x\rightarrow \infty }\sqrt{x+\sqrt{x}}+\sqrt{x}$
• Aug 24th 2010, 04:41 AM
Prove It
Hints:
Limit of a power = Power of the limit.
Limit of a sum = Sum of the limit.
• Aug 24th 2010, 04:43 AM
banku12
i did not get
• Aug 24th 2010, 04:50 AM
Prove It
A square root is the same as taking to the power of $\displaystyle \frac{1}{2}$.

So now use the fact that the limit of the power is the same as the power of the limit.
• Aug 24th 2010, 05:19 AM
chisigma
May be that there is a '+' instead of a '-' and the limit is...

$\displaystyle \displaystyle \lim_{x \rightarrow \infty} \sqrt{x + \sqrt{x}} - \sqrt {x}$ (1)

In that case is...

$\displaystyle \displaystyle \lim_{x \rightarrow \infty} \sqrt{x + \sqrt{x}} - \sqrt {x}= \lim_{x \rightarrow \infty} \frac{\sqrt{x}}{\sqrt{x + \sqrt{x}} + \sqrt {x}} =$

$\displaystyle \displaystyle = \lim_{x \rightarrow \infty} \frac{1}{1 + \sqrt{1 + \frac{1}{\sqrt{x}}}} = \frac{1}{2}$ (2)

Kind regards

$\displaystyle \chi$ $\displaystyle \sigma$