Calc

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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 -

    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 -

    Oh, I forgot all about L'Hospital's Rule. Thanks!

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