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sparky34
sparky34 asked in Science & MathematicsMathematics · 8 years ago

Can some one explain this limit to me? Calculus.?

lim (____1___)^(1/(bx))

x->0 ( ax+1 )

a and b are constants

1 Answer

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  • Iggy Rocko
    Lv 7
    8 years ago
    Favorite Answer

    L = lim (1/(ax + 1))^(1/(bx))

    .....x-> 0

    lnL = lim ln((1/(ax + 1))^(1/(bx)))

    ........x-> 0

    lnL = lim ln(1/(ax + 1))/(bx)...now use L'Hopital's rule

    ........x-> 0

    lnL = lim (a/(ax + 1))/b

    ........x-> 0

    lnL = lim a/(abx + b)

    ........x-> 0

    lnL = a/b

    e^(lnL) = e^(a/b)

    L = e^(a/b)

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