What is the simplified form of the limit as x approaches infinity?

[karush]

$$\lim_{x\to +\infty}\sqrt{x^2+3}-x$$

sorry first of all how do you turn this string into latex
I don't see the icon tool on the editor

thnx

 

[awkward]

$$\lim_{x\to +\infty}\sqrt{x^2+3}-x}$$

sorry first of all how do you turn this string into latex
I don't see the icon tool on the editor

thnx

$$\lim_{x \to +\infty} \sqrt{x^2+3}-x$$

Click on Reply With Quote to see the LaTex. Or better yet, there is a "How To Use LaTex on This Site" thread in the LaTeX Help section of the site.

Hint: Try multiplying by $$ \frac{\sqrt{x^2+3} + x}{\sqrt{x^2+3} + x} $$

 

[checkitagain]

$$\lim_{x\to +\infty}{(\sqrt{x^2 + 3} - x)}$$

Redo post:Alternative
Using the Binomial Theorem for $$(x^2 + 3)^{\frac{1}{2}},$$

write the limit as $$\displaystyle\lim_{x\to +\infty}{\bigg(x + \dfrac{3}{2x} + (all \ \ other \ \ terms \ \ with \ \ degree \ \ less \ \ than \ \ -1) \ - \ x \bigg)}$$