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

That is limit I am talking about.

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

getting me ??

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

I can not quite follow you here.

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

yup

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

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

nevermind,,glad to help ! :)