## Limits with Square roots Question help

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?
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 Recognitions: Gold Member Science Advisor Staff Emeritus 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 $$\frac{\sqrt{x^2+ 4x}- x(cos(x))}{1}$$ and "rationalize the numerator"- multiply numerator and denominator by $$\sqrt{x^2+ 4x(cos(x)}+ x$$.
 thanks mate :) im pretty noob at calculus. :( EDIT: what happened to the cos x in the equation?

## Limits with Square roots Question help

bump
 Recognitions: Gold Member Science Advisor Staff Emeritus Sorry I accidently dropped it. I have edited my previous posts: Multiply numerator and denominator by $$\sqrt{x^2+ 4x(cos(x)}+ x$$.
 Hi, thanks for correcting that mistake, but should i apply L'Hopitals rule in this case? i cant tell :(

 Tags calculus, cos x, limit, limits, square roots