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Limits with Square roots Question help 
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#1
Apr911, 06:09 AM

P: 5

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? 


#2
Apr911, 06:28 AM

Math
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PF Gold
P: 39,348

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]. 


#3
Apr911, 06:29 AM

P: 5

thanks mate :) im pretty noob at calculus. :(
EDIT: what happened to the cos x in the equation? 


#4
Apr911, 07:16 AM

Math
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PF Gold
P: 39,348

Limits with Square roots Question help
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]. 


#5
Apr911, 07:25 AM

P: 5

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



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