# limit of function - please explain

• Dec 21st 2012, 10:21 PM
muddywaters
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 $\displaystyle a\leq0 ,\lim_{n \to \infty}f(x)=+\infty$'??
• Dec 21st 2012, 10:28 PM
chiro
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?
• Dec 22nd 2012, 04:53 AM
muddywaters
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?
• Dec 22nd 2012, 09:01 AM
hollywood
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