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Math Help - limits with the e exponnent

  1. #1
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    limits with the e exponnent

    I have trouble with these can anyone help me work out this problem.
    lim e^((5x^2+sinx)/(x^2+20))
    x-infinity

    Thanks in advance.
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  2. #2
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    Quote Originally Posted by macro View Post
    I have trouble with these can anyone help me work out this problem.
    lim e^((5x^2+sinx)/(x^2+20))
    x-infinity

    Thanks in advance.
    ignore the exponent's base for a moment ... what is this limit?

    \lim_{x \to \infty} \frac{5x^2 + \sin{x}}{x^2 + 20}
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  3. #3
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    it's 5 right since its the principle term?
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    Quote Originally Posted by macro View Post
    it's 5 right since its the principle term?
    correct.

    so, what is \lim_{x \to \infty} e^{\frac{5x^2+\sin{x}}{x^2+20}} ?
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  5. #5
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    Is the limit e^5 since its a constant?
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  6. #6
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    Quote Originally Posted by macro View Post
    Is the limit e^5 since its a constant?
    yes, the limit is e^5 ... I don't know what you mean by "it's a constant"

    the limit is just a property of composite functions ...

    if \lim_{x \to \infty} f(x) = 5 , then \lim_{x \to \infty} e^{f(x)} = e^5
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  7. #7
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    oh ok thanks a bunch
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  8. #8
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    The crucial point is that e^x is a continuous function:
    \lim_{x\to a}e^{f(x)}= e^{\lim_{x\to a} f(x)}.
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