What is the limit as x approaches 81 of ((\sqrt[4]{x}-3))/(x-81) ?

The limit as x approaches 81 of ((\sqrt[4]{x}-3))/(x-81) is 1/108

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limit as x approaches 81 of ((\sqrt[4]{x}-3))/(x-81)

\frac{1}{108}

Decimal Notation

0.00925 \dots

Solution steps

Apply L'Hopital's Rule

: x \to 81 lim (\frac{\frac{1}{4 x ^{\frac{3}{4}}}}{1})

= x \to 81 lim (\frac{\frac{1}{4 x ^{\frac{3}{4}}}}{1})

Plug in the value

x = 81

= \frac{\frac{1}{4 \cdot 8 1 ^{\frac{3}{4}}}}{1}

Simplify

\frac{\frac{1}{4 \cdot 8 1 ^{\frac{3}{4}}}}{1} : \frac{1}{108}

= \frac{1}{108}

\frac{\partial}{\partial u} (b ((\frac{( N u )}{V ( u )})^{(\frac{2}{3})}))

\int_{1}^{\infty} \frac{1}{x ^{2}} d x

ln (x + 1), 2

\frac{\partial}{\partial x} (\frac{x ^{2}}{( y - x ) ^{2}})

n = 1 \sum \infty \frac{2}{n ^{8}}

What is the limit as x approaches 81 of ((\sqrt[4]{x}-3))/(x-81) ?
The limit as x approaches 81 of ((\sqrt[4]{x}-3))/(x-81) is 1/108