Limits with Square roots Question help

Sleighty

1. The problem statement, all variables and given/known data

lim x -> infinity : sqrt(x^2 + 4x(cos x) ) - x

find the limit (or lack there of)

2. Relevant equations

look above

3. The attempt at a solution

ok so i used the addition/subtraction law to show that the limit of f(x) = - x as x --> infinity = infinity

now for the other half of the function, i cant seem to find out how to mathematically prove that there is no limit. logically i can tell that there is no limit because COS X has no limit.

can someone explain how i prove this mathematically?

HallsofIvy

You are completely wrong about this problem- you cannot use the "addition/subtraction" law here because you cannot add/subtract "infinity".

Think of this as the fraction
[tex]\frac{\sqrt{x^2+ 4x}- x(cos(x))}{1}[/tex]
and "rationalize the numerator"- multiply numerator and denominator by
[tex]\sqrt{x^2+ 4x(cos(x)}+ x[/tex].

Sleighty

thanks mate :) im pretty noob at calculus. :(

EDIT: what happened to the cos x in the equation?

Sleighty

bump

HallsofIvy

Sorry I accidently dropped it. I have edited my previous posts:
Multiply numerator and denominator by
[tex]\sqrt{x^2+ 4x(cos(x)}+ x[/tex].

Sleighty

Hi, thanks for correcting that mistake, but should i apply L'Hopitals rule in this case? i cant tell :(