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Maths-

General

Easy

Question

$Lt subscript x not stretchy rightwards arrow 1 end subscript invisible function application fraction numerator cube root of x minus 1 over denominator x minus 1 end fraction$

$\frac{2}{3}$
$\frac{3}{2}$
$\frac{1}{3}$
$\frac{1}{2}$

The correct answer is: $2 over 3$

$limit as x rightwards arrow 1 of fraction numerator cube root of x minus 1 over denominator x minus 1 end fraction equals limit as x rightwards arrow 1 of fraction numerator cube root of x minus cube root of 1 over denominator open parentheses cube root of x close parentheses cubed minus open parentheses cube root of 1 close parentheses cubed end fraction equals limit as x rightwards arrow 1 of fraction numerator cube root of x minus cube root of 1 over denominator open parentheses cube root of x minus cube root of 1 close parentheses open parentheses open parentheses x close parentheses to the power of begin display style 2 over 3 end style end exponent plus open parentheses x close parentheses to the power of begin display style 1 third end style end exponent plus 1 close parentheses end fraction equals limit as x rightwards arrow 1 of open parentheses fraction numerator 1 over denominator open parentheses open parentheses x close parentheses to the power of 2 over 3 end exponent plus open parentheses x close parentheses to the power of 1 third end exponent plus 1 close parentheses end fraction close parentheses equals fraction numerator 1 over denominator 1 plus 1 plus 1 end fraction equals 1 third$

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