Need help finding the limit as X approaches positive infinity

[abel muroi]

I was given this problem..



(x - 3)/(SquareRoot(4x² + 3))



And i was asked to find the limit as X approaches Positive infinity.




I usually understand these kinds of problems, and I know i'm supposed to divide every number in the fraction by the highest degree term in the denominator. But the squareroot threw me off completely.

How can i start to solve this?

(Btw I know the answer is 1/2... but i want to know the steps that are required to get to the answer)

 

[Ishuda]

I was given this problem..



(x - 3)/(SquareRoot(4x² + 3))



And i was asked to find the limit as X approaches Positive infinity.




I usually understand these kinds of problems, and I know i'm supposed to divide every number in the fraction by the highest degree term in the denominator. But the squareroot threw me off completely.

How can i start to solve this?

(Btw I know the answer is 1/2... but i want to know the steps that are required to get to the answer)

The expression SquareRoot(4x² + 3) can be written as 2 x SquareRoot(1 + 3/(4x²)).

 

[pka]

I was given this problem..(x - 3)/(SquareRoot(4x² + 3))
And i was asked to find the limit as X approaches Positive infinity.

If $\displaystyle x\to\infty$ then $\displaystyle x>0$ divide by $\displaystyle x$ to get
$\displaystyle \dfrac{1-3x^{-1}}{\sqrt{4+3x^{-2}}}$ from which the limit should be clear.