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? asked in Science & MathematicsMathematics · 2 years ago

What is the limit of 10x^(6/x) as x goes to infinity using L Hopital s Rule?

1 Answer

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  • kb
    Lv 7
    2 years ago

    Let L = lim(x→∞) x^(6/x).

    Take the natural log of both sides:

    ln L = lim(x→∞) ln(x^(6/x))

    .......= lim(x→∞) (6/x) ln x

    .......= lim(x→∞) 6 ln(x)/x

    .......= lim(x→∞) 6 (1/x)/1, by L'Hopital's Rule (∞/∞ type)

    .......= 0.

    So, L = e^0 = 1.

    Finally, lim(x→∞) 10x^(6/x) = 10 * 1 = 10.

    I hope this helps!

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