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Math Help - Limits at Infinity

  1. #1
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    Limits at Infinity

    in my textbook it says this:

    lim x-->infinty square root (x^2+x) - x **note the x^2+x is under the root only

    is the same as square root (x^2) - x **the x^2 is under the root only

    which is lim x--> infinity (x-x) = 0

    Question 1: Can someone please explain how we get 0 (especially the part where square root(x^2+x) becomes square root(x^2)


    Question 2: under this example in the book it says "it can be shown that the limit in the above question is not 0 but is 1/2 --?? what the heck does that mean they just showed that it equals 0 now they're saying it equals 1/2 ??

    can someone explain both please
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  2. #2
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by alisheraz19 View Post
    in my textbook it says this:

    lim x-->infinty square root (x^2+x) - x **note the x^2+x is under the root only

    is the same as square root (x^2) - x **the x^2 is under the root only

    which is lim x--> infinity (x-x) = 0

    Question 1: Can someone please explain how we get 0 (especially the part where square root(x^2+x) becomes square root(x^2)


    Question 2: under this example in the book it says "it can be shown that the limit in the above question is not 0 but is 1/2 --?? what the heck does that mean they just showed that it equals 0 now they're saying it equals 1/2 ??

    can someone explain both please
    I think in the first instance they were probably talking about a mistake that students would probably make. while 1/2 is the actual answer. to get that 1/2 is the answer, the first step would be to multiply by \frac {\sqrt{x^2 + x} + x}{\sqrt{x^2 + x} + x}
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