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Math Help - Limit Problem. Please Help.

  1. #1
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    Please delete this thread. Posted in wrong forum.

    lim x-> infinity [ |9+5x-6x^2| ] / [ 2x^2 - xsinx ]

    i get 0 as answer. Firstly I used Hopital rule, and then i factor out x^2 before getting 0 as answer. But i think im wrong, can any one help?

    I did not just factor out x^2 initially, because if i do that, for the xsinx term in the denominator, it becomes (sinx)/x. And if you take x-> infinity to (sinx)/x, doesnt it give u infinity/infinity and not 0?
    Last edited by toffeefan; February 22nd 2010 at 06:10 AM.
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  2. #2
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    Quote Originally Posted by toffeefan View Post
    lim x-> infinity [ |9+5x-6x^2| ] / [ 2x^2 - xsinx ]

    i get 0 as answer. Firstly I used Hopital rule, and then i factor out x^2 before getting 0 as answer. But i think im wrong, can any one help?

    I did not just factor out x^2 initially, because if i do that, for the xsinx term in the denominator, it becomes (sinx)/x. And if you take x-> infinity to (sinx)/x, doesnt it give u infinity/infinity and not 0?
    No, it doesn't. sin(x) does NOT go to infinity- it stays between 1 and -1. (sin x)/x definitely goes to 0 as x goes to infinity. My recommendation, go ahead and divide both numerator and denominator by x^2 as you say. That gives
    \frac{|\frac{9}{x^2}+ \frac{5}{x}- 6|}{2- \frac{sin x}{x}} and now everything that still involves an "x" will go to 0.
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