What is the limit as x approaches 1 of (1-x)/(\sqrt[3]{8x^3-8)} ?

The limit as x approaches 1 of (1-x)/(\sqrt[3]{8x^3-8)} is 0

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limit as x approaches 1 of (1-x)/(\sqrt[3]{8x^3-8)}

0

Solution steps

Rationalize denominator

= x \to 1 lim - \frac{( x ^{3} - 1 ) ^{\frac{2}{3}}}{2 ( x ^{2} + x + 1 )}

Plug in the value

x = 1

= - \frac{( 1 ^{3} - 1 ) ^{\frac{2}{3}}}{2 ( 1 ^{2} + 1 + 1 )}

Simplify

- \frac{( 1 ^{3} - 1 ) ^{\frac{2}{3}}}{2 ( 1 ^{2} + 1 + 1 )} : 0

= 0

What is the limit as x approaches 1 of (1-x)/(\sqrt[3]{8x^3-8)} ?
The limit as x approaches 1 of (1-x)/(\sqrt[3]{8x^3-8)} is 0