Posted by Anna on .
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.
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
√((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
Oh, I forgot all about L'Hospital's Rule. Thanks!