# [SOLVED]limit with square root

#### karush

##### Well-known member
$$\lim_{x\to +\infty}\sqrt{x^2+3}-x$$

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

thnx

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#### awkward

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

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 $$\frac{\sqrt{x^2+3} + x}{\sqrt{x^2+3} + x}$$

Last edited:

#### checkittwice

##### Member
$$\lim_{x\to +\infty}{(\sqrt{x^2 + 3} - x)}$$
Redo post:

Alternative

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

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