L'Hopital's Rule

P

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I'm stuck with this particular problem involving limits and L'Hopital's Rule.

This is the problem

Lim [(x^2 + 4)^1/2] / x
x-->infinity

This is infinity over infinity so I apply L'Hopital's Rule

I find the derivative which I get

lim x / (x^2 + 4)^1/2
x-->infinity

If I evaluate x as it approaches infinity then the numerator is infinity but i'm stuck with the denominator. I'm thinking it's gonna be infinity over a number but I'm not sure. Any help is much appreciated. Thanx
 
Why not note that [(x<SUP>2</SUP>+4)<SUP>1/2</SUP>] /x=([x<SUP>2</SUP>+4]/x<SUP>2</SUP>)<SUP>1/2</SUP>.
 
I'm not sure but if it's [(x^2 + 4)/x^2]^1/2, then the limit is 1. Am I correct?
 
Please show me why you think the limit would be 1. This is calc 2, right?
 
Calc 1. I was thinking divide the terms in the numerator and denominator by the highest power, x^2. So i'm left with (1)^1/2 which is 1.
 
Hooray :D . I hate limits, it just doesn't click so I'll have to practice more. But I didn't know that I could square that x from the denominator.
 
Actually, had you noticed
y = Lim [(x^2 + 4)^1/2] / x

y = lim x / (x^2 + 4)^1/2 = 1/y

y^2=1
--------------------
Gene
 
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