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find-lim-x-0-a-x-b-x-e-ax-e-bx-with-a-gt-0-b-gt-0-and-a-b-




Question Number 40111 by maxmathsup by imad last updated on 15/Jul/18
find  lim _(x→0)    ((a^x  −b^x )/(e^(ax)  −e^(bx) ))   with a>0    b>0  and a≠b
$${find}\:\:{lim}\:_{{x}\rightarrow\mathrm{0}} \:\:\:\frac{{a}^{{x}} \:−{b}^{{x}} }{{e}^{{ax}} \:−{e}^{{bx}} }\:\:\:{with}\:{a}>\mathrm{0}\:\:\:\:{b}>\mathrm{0}\:\:{and}\:{a}\neq{b} \\ $$

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