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Math Help - Finding the answer to a Limit

  1. #1
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    Finding the answer to a Limit

    Find lim->0 (2+5/x2)
    This is what I did first.
    I first plugged in 0 to find if it's true.
    2+5/0
    Of course it's undefined since you can't divide by 0
    So I was confused... How do you do this then?

    Because if you factor x2, it'll be (x)(x) which will be 0 = undefined
    Can someone explain please?
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  2. #2
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    Re: Finding the answer to a Limit

    you don't actually divide by 0. The concept of taking a limit is going towards 0, but you have to think you will never actually reach that number. How you need to think about it is that you're dividing 2+5 by a number extremely small. So the answer is infinity. Any number divided by something infinitely small will yield an extremely huge number. Hence as you approach 0, (2+5)/x^2 tends to infinity.
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  3. #3
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    Re: Finding the answer to a Limit

    Oh oops, it was actually 2+(5/x^2)
    But I see, thanks
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  4. #4
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    Re: Finding the answer to a Limit

    The more interesting problems occur when you get X occuring more than once,

    eg Lim x->inf [(x^2+1)/x]-x = 0

    Can be solved as below,

    Lim x->inf = x^2/x + 1/X -X

    X^2/X =X
    1/X=0

    Lim x->inf= X + 0 -X = 0
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