## anonymous 3 years ago lim_{x rightarrow infty} (-3x+sqrt{9x^2+4x-5}) The answer is apparently 2/3. But I can´t loose the squareroot term at any place so I always end up with infinity - infinity = 0. How do I do this limit right?

1. anonymous

$\lim_{x \rightarrow \infty} (-3x+\sqrt{9x^2+4x-5})$

2. anonymous

That is limit I am talking about.

3. shubhamsrg

rationalize it.. see if it it helps..which it should..

4. shubhamsrg

getting me ??

5. anonymous

I guess... let me show your where I stuck right now.

6. shubhamsrg

you're right till there.. now,, take x^2 common from the sqrt and in all,, x common from the denominator,, you see the solution now ?

7. anonymous

I can not quite follow you here.

8. shubhamsrg

you have (4x)/(sqrt(9x^2 +4x -5) + 3x) = (4x)( x sqrt( 9 + 4/x - 5/x^2 ) + 3x following till here ?

9. anonymous

yup

10. shubhamsrg

now,,x gets cancelled from numerator and denominator .. is much easier then right ?

11. anonymous

Ah... now I understand. Thanks a lot shubhamsrg. I never thought of doing that one. :) thx

12. shubhamsrg