How to find the right and left limit of lim x--3 (sqrt(x)-sqrt(3))/(x-3) +3x^2 ?

Question

How to find the right and left limit of lim x-->3 (sqrt(x)-sqrt(3))/(x-3) +3x^2 ?

anonymous · Answer

$$\lim_{x \rightarrow 3} (\sqrt{x}-\sqrt{3})\div( x-3) + 3x^{2}$$

mathmale · Answer

Please clarify:  are you dividing by [ (x-3) + 3x^2 ] or only by (x-3).  If the former, then please make that clear by using another set of parentheses to enclose the denominator.
This math problem is from what course?

anonymous · Answer

$$\lim_{x\to3}\left(\frac{\sqrt x-\sqrt3}{x-3}+3x^2\right) ~~?$$

anonymous · Answer

oops sorry! yes, what sithsandgiggles posted is how the equation should be set up.

anonymous · Answer

and this is from calc 1.

mathmale · Answer

You'll get faster (and perhaps better) responses from potential helpers if you'd please be certain that the expression you type in is in no way ambiguous.

mathmale · Answer

As x approaches 3, 3x^2 approaches 27.  That's the easy part.

As for the first term within parentheses:  Try factoring x-3.  
Hint:  Note that Sqrt(x)-Sqrt(3) is one of the factors of x-3.

anonymous · Answer

So could I factor it as $$(\sqrt{x}-\sqrt{3})(\sqrt{x}-\sqrt{3})$$ to get x-3?

anonymous · Answer

oops, i meant to put a plus instead of a minus for one of the factors.