# Limits with Square roots Question help

## Homework Statement

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

find the limit (or lack there of)

look above

## 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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HallsofIvy
Homework Helper

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

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

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

HallsofIvy
$$\sqrt{x^2+ 4x(cos(x)}+ x$$.