limit of function - please explain

Let $\displaystyle f(x)=\sqrt{4x^2-12x+11}-ax-b$

when $\displaystyle a\leq0 ,\lim_{n \to \infty}f(x)=+\infty$

my book gave me this without any further explanation. how do we get 'when $\displaystyle a\leq0 ,\lim_{n \to \infty}f(x)=+\infty$'??

could be something simple that i overlooked >.< please help

Re: limit of function - please explain

Hey muddywaters.

The short answer is that the square root term approaches infinity and since a <= 0 we have a situation where - (-x) = +x which means -ax > 0 which leaves infinity + infinity - constant = infinity.

What you may want to do however is use L'hopitals rule: have you used this before?

Re: limit of function - please explain

thanks. no i have not learned that yet. maybe in a coming topic.just to confirm - every square root term that has x will surely approach infinity as x approaches infinity right?

Re: limit of function - please explain

What you said is too general. Let's say if some function $\displaystyle f(x)$ goes to infinity as x goes to infinity, then $\displaystyle \sqrt{f(x)}$ also goes to infinity as x goes to infinity.

- Hollywood