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Math Help - [SOLVED] limit as x approaches infinity w/ e

  1. #1
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    [SOLVED] limit as x approaches infinity w/ e

    I am not getting anywhere I have this:
    limit as x approaches infinity of (8+18e^3x)/(25e^5x+4) I keep applying L'Hopital's Rule but I just keep getting infinity over infinity.
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  2. #2
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    Quote Originally Posted by Amberosia32 View Post
    I am not getting anywhere I have this:
    limit as x approaches infinity of (8+18e^3x)/(25e^5x+4) I keep applying L'Hopital's Rule but I just keep getting infinity over infinity.
    Applying L'Hospital's Rule is fine...

    \lim_{x \to \infty}\frac{8 + 18e^{3x}}{25e^{5x} + 4}

     = \lim_{x \to \infty}\frac{54e^{3x}}{125e^{5x}} by L'Hospital

     = \lim_{x \to \infty}\frac{54}{125e^{2x}} by cancelling


    What happens as the denominator gets infinitely large?
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  3. #3
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    Quote Originally Posted by Prove It View Post
    Applying L'Hospital's Rule is fine...

    \lim_{x \to \infty}\frac{8 + 18e^{3x}}{25e^{5x} + 4}

     = \lim_{x \to \infty}\frac{54e^{3x}}{125e^{5x}} by L'Hospital

     = \lim_{x \to \infty}\frac{54}{125e^{2x}} by cancelling


    What happens as the denominator gets infinitely large?
    I didn't even think of canceling. Wow I feel really dumb, thanks so much.
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