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Right Hand Limit

Question

Evaluate: $lim x \to 0 {(\frac{a^{x} + b^{x} + c^{x}}{3})}^{2 / x}$
$(a b c)^{1 / 3}$
$(a b c)^{2}$
$(a b c)^{2 / 3}$
$a + b + c$

A

(a b c)^{2}

B

a + b + c

C

(a b c)^{1 / 3}

D

(a b c)^{2 / 3}

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Solution

Verified by Toppr

$lim x \to 0 {(\frac{a^{x} + b^{x} + c^{x}}{3})}^{2 / x} = {(\frac{3}{3})}^{2 / 0}$

$= 1^{\infty}$ form
$= e^{lim x \to 0 {(\frac{a^{x} + b^{x} + c^{x}}{3} - 1)}^{2 / x}}$

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