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Question Number 30748 by abdo imad last updated on 25/Feb/18

let a>0 and b>0 find lim_(x→0^+ )   (  ((a^x  +b^x )/2))^(1/x)   .

$${let}\:{a}>\mathrm{0}\:{and}\:{b}>\mathrm{0}\:{find}\:{lim}_{{x}\rightarrow\mathrm{0}^{+} } \:\:\left(\:\:\frac{{a}^{{x}} \:+{b}^{{x}} }{\mathrm{2}}\right)^{\frac{\mathrm{1}}{{x}}} \:\:. \\ $$

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