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Math Help - Find the limit of square root

  1. #1
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    Find the limit of square root

    The question is to find the limit as x->inf of x/sqr(1+(x/c)^2) where c is a constant. I rewrote the equation as sqr(x^2*c^2/(x^2+c^2)). Then find the limit of what is inside the square root ie. x^2*c^2/(x^2+c^2). This comes to c^2 the square root of which is c.

    Is this the correct and most appropriate way of arriving at the limit?
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  2. #2
    is up to his old tricks again! Jhevon's Avatar
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    A bit unorthodox, but that works. you forgot one thing though: \sqrt{c^2} = |c|
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  3. #3
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    I thought it may be somewhat unorthodox. What would be a more common method?
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  4. #4
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    Divide both the numerator and denominator by x. (Just x because it'll get squared when it goes under the square root and kill the x^2 under the square root in the denominator).

    \lim_{x \rightarrow \infty} \frac{x}{\sqrt{1+(x/c)^2}} = \lim_{x \rightarrow \infty} \frac{1}{\sqrt{1/x^2+(1/c)^2}} = \frac{1}{\sqrt{(1/c)^2}} = |c|
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  5. #5
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    Quote Originally Posted by nehme007 View Post
    Divide both the numerator and denominator by x. (Just x because it'll get squared when it goes under the square root and kill the x^2 under the square root in the denominator).

    \lim_{x \rightarrow \infty} \frac{x}{\sqrt{1+(x/c)^2}} = \lim_{x \rightarrow \infty} \frac{1}{\sqrt{1/x^2+(1/c)^2}} = \frac{1}{\sqrt{(1/c)^2}} = |c|
    Less algebraic manipulation required with this method and therefore quicker and better.
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