Homework Help: Calc

Posted by Anna on Friday, May 25, 2012 at 12:44pm.

Find the limit as x approaches zero from the right of ((sqrt((1+x)/(x^2))-(1/x))

I don't even know where to start with this. Help?

P.S. If you go to the wolfphram alpha website and put copy and paste ((sqrt((1+x)/(x^2))-(1/x)) into the search bar you can see what it looks like.

Thanks!

Calc - Steve, Friday, May 25, 2012 at 1:20pm
as long as you're at wolframalpha, type in

limit x->0+ (sqrt((1+x)/(x^2))-(1/x))

and see that the limit is 1/2. The question is, how do you figure it?

√((1+x)/x^2) = √(1+x)/x
so,

√((1+x)/(x^2))-(1/x) = √(1+x)/x - 1/x
= (√(1+x) - 1)/x

As x->0, the fraction is 0/0, so use L'Hospital's Rule to get

1/(2√(1+x)) / 1 = 1/2
Calc - Anna, Friday, May 25, 2012 at 1:53pm
Oh, I forgot all about L'Hospital's Rule. Thanks!

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