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Math Help - limit of function - please explain

  1. #1
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    limit of function - please explain

    Let f(x)=\sqrt{4x^2-12x+11}-ax-b
    when a\leq0 ,\lim_{n \to \infty}f(x)=+\infty

    my book gave me this without any further explanation. how do we get 'when a\leq0 ,\lim_{n \to \infty}f(x)=+\infty'??
    could be something simple that i overlooked >.< please help
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  2. #2
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    Re: limit of function - please explain

    Hey muddywaters.

    The short answer is that the square root term approaches infinity and since a <= 0 we have a situation where - (-x) = +x which means -ax > 0 which leaves infinity + infinity - constant = infinity.

    What you may want to do however is use L'hopitals rule: have you used this before?
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  3. #3
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    Re: limit of function - please explain

    thanks. no i have not learned that yet. maybe in a coming topic.just to confirm - every square root term that has x will surely approach infinity as x approaches infinity right?
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  4. #4
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    Re: limit of function - please explain

    What you said is too general. Let's say if some function f(x) goes to infinity as x goes to infinity, then \sqrt{f(x)} also goes to infinity as x goes to infinity.

    - Hollywood
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