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Math Help - Problem with limit

  1. #1
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    Problem with limit

    I dont understand how to solve excercises of limit.
    I know the answer is 0 but I dont know how this answer is derived.
    1/0= undefined

    How can I control if this answer is right ?
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  2. #2
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    Quote Originally Posted by totalnewbie View Post
    I dont understand how to solve excercises of limit.
    I know the answer is 0 but I dont know how this answer is derived.
    1/0= undefined

    How can I control if this answer is right ?
    Let us think about this.

    What is,
    \lim_{x\to 0^+}2^{1/x}=?
    The function increases without bound.
    Thus,
    \frac{1}{1+2^{1/x}}\to 0
    Because the denominator get larger and larger and larger.
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  3. #3
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    You have to pay attention to the fact that {x\to+0} and not 0. Let's see what {x\to+0} means. Yes, x is about zero, but a positive. It's like 0.00000000...00001, and 1/x=1,000,000,000...,000. A very large positive number, thus infinity.
    So, {2^{\frac {1}{x}}} is is going to be a very large number, infinity. Therfore, dividing a finit number by a very large one is going to give as 0.
    Hope this helps!
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