FInd lim. Apply 1'hopital's rule as many times as necessary, verifying your result after each application

lim e^2x/(x+5)^3


1 Answer

  • Anonymous
    1 decade ago
    Favorite Answer

    This goes to ∞ / ∞, so we can apply l'Hopital's rule. Take the derivative of the top and bottom:

    2e^(2x) / 3(x+5)^2

    This too goes to ∞ / ∞, so apply l'Hopital's rule again.

    4e^(2x) / 6(x+5) = 4e^(2x) / (6x+30)

    This goes to ∞ / ∞, so apply l'Hopital's rule once again.

    8e^(x) / (6)

    This grows without bound, therefore the original expression has no limit.

    It's important to keep checking at every step that the limit appears to go to ∞ / ∞ or 0/0, otherwise you can't apply the rule.

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