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Math Help - "very difficult" limits question

  1. #16
    Senior Member polymerase's Avatar
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    Quote Originally Posted by topsquark View Post
    Check that again:
    \lim_{x \to \infty} \dfrac{5x^2}{\sqrt[3]{{\left( {x^3 + 5x^2 } \right)^2 }} + x\sqrt[3]{{x^3 + 5x^2 }} + x^2 }

    = \lim_{x \to \infty} \dfrac{5}{\frac{1}{x^2}\sqrt[3]{{\left( {x^3 + 5x^2 } \right)^2 }} + \frac{1}{x}\sqrt[3]{{x^3 + 5x^2 }} + 1 }

    = \lim_{x \to \infty} \dfrac{5}{\sqrt[3]{{\left( {1 + \frac{5}{x} } \right)^2 }} + \sqrt[3]{{1 + \frac{5}{x} }} + 1 }

    = \frac{5}{1 + 1 + 1} = \frac{5}{3}

    -Dan
    thank you
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  2. #17
    Math Engineering Student
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    Quote Originally Posted by polymerase View Post
    ....wow how do you come up with something like this to solve this question? i have never seen anyone rationalize like this before
    It's a well known trick.

    It's based using the identity a^3-b^3=(a-b)(a^2+ab+b^2)
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  3. #18
    Forum Admin topsquark's Avatar
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    Quote Originally Posted by Krizalid View Post
    It's a well known trick.

    It's based using the identity a^3-b^3=(a-b)(a^2+ab+b^2)
    "Well known" he calls it!

    I had to "invent" the method for myself once when I was teaching a College Algebra course.

    They don't teach us poor Physicists anything!

    -Dan
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  4. #19
    Math Engineering Student
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    ?

    What ?

    Sorry, but I thought it was well known xD!
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  5. #20
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by Krizalid View Post
    It's a well known trick.

    It's based using the identity a^3-b^3=(a-b)(a^2+ab+b^2)
    hehe, i laughed at that too, topsquark


    you seem to have tweeked the eqution though. because here, "b^2" should have been "x^{2/3}" i think, you have just "x^2" ...but anyway, i kind of see where you're coming from

    Quote Originally Posted by Krizalid View Post
    ?

    What ?

    Sorry, but I thought it was well known xD!
    perhaps for you

    Quote Originally Posted by Krizalid View Post
    You're wrong
    haha, and he said that with a smile. that was great!

    you are the man, Krizalid!!!
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