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## Homework Statement

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

find the limit (or lack there of)

## Homework Equations

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?