What is the limit as x approaches 1 of ((\sqrt[6]{x}-1))/(x-1) ?

The limit as x approaches 1 of ((\sqrt[6]{x}-1))/(x-1) is 1/6

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limit as x approaches 1 of ((\sqrt[6]{x}-1))/(x-1)

x \to 1 lim (\frac{( 6 x - 1 )}{x - 1})

\frac{1}{6}

Decimal

0.16666 \dots

Solution steps

x \to 1 lim (\frac{6 x - 1}{x - 1})

Apply L'Hopital's Rule

: x \to 1 lim (\frac{\frac{1}{6 x ^{\frac{5}{6}}}}{1})

= x \to 1 lim (\frac{\frac{1}{6 x ^{\frac{5}{6}}}}{1})

Plug in the value

x = 1

= \frac{\frac{1}{6 \cdot 1 ^{\frac{5}{6}}}}{1}

Simplify

= \frac{1}{6}

y^{^{''}} + 10 y^{^{'}} + 9 y = 9

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\frac{d}{d x} (2 a x - \frac{1}{x ^{2}})

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What is the limit as x approaches 1 of ((\sqrt[6]{x}-1))/(x-1) ?
The limit as x approaches 1 of ((\sqrt[6]{x}-1))/(x-1) is 1/6