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${Lim}_{x \to \infty} {(\frac{a^{1 / x} + b^{y_{x}} + c^{y_{x}}}{3})}^{x} = (where a_{~} b,c are real and non-zero)$

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(abc)1/3

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Correct option is B

limx→∞a1/x+b1/x+c1/x3xelimx→∞xa1/x+b1/x+c1/x3−1=elimx→∞xa1/x+b1/x+c1/x−33=elimx→∞xa1/x−1+b1/x−1+c1/x−13=elimx→∞13a1/x−11x+b1/x1x+c1/x1x=elimx→∞ 13(log⁡a+log⁡b+log⁡c)=e13(log⁡abc)=elog⁡(abc)13=(abc)13

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Limx→∞⁡a1/x+byx+cyx3x= where a~ b,c are real and non-zero)

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${Lim}_{x \to \infty} {(\frac{a^{1 / x} + b^{y_{x}} + c^{y_{x}}}{3})}^{x} = (where a_{~} b,c are real and non-zero)$