## mortonsalt one year ago Hello! I was wondering if someone can help me with this question? (Will be posted below.)

1. mortonsalt

Find the limit as it approaches infinity when $\frac{4x-1}{x} < f(x) < \frac{4x^2+3x}{x^2}$ for all x>5.

2. anonymous

you need to find out what x is?

3. anonymous

4. mortonsalt

Im just trying to figure out where to begin. :) Thank you!

5. anonymous

@welshfella

6. anonymous

7. mortonsalt

Is it 4?

8. anonymous

no

9. welshfella

sorry cant help with this one

10. anonymous

lol

11. anonymous

is this a multiple choice question?

12. mortonsalt

Nope!

13. anonymous

ok good

14. anonymous

10x^2

15. mortonsalt

Alright, thanks!

16. anonymous

:D

17. zepdrix

Take limit of left side,$\large\rm \lim\limits_{x\to\infty}\frac{4x-1}{x}=a$It will approach some value. Take limit of the other side,$\large\rm \lim\limits_{x\to\infty}\frac{4x^2+3x}{x^2}=a$You'll find that they approach the same value! So by Squeeze Theorem: $$\large\rm f(x)\to a$$ as $$\large\rm x\to\infty$$. It's a little disturbing that you have strict inequalities.. those shouldn't be strict. Maybe a typo? Anyway, yes 4 sounds right! :)