What is the limit as x approaches 1 of (\sqrt[3]{x+7}-2)/(x^3-1) ?

The limit as x approaches 1 of (\sqrt[3]{x+7}-2)/(x^3-1) is 1/36

Popular >

limit as x approaches 1 of (\sqrt[3]{x+7}-2)/(x^3-1)

x \to 1 lim (\frac{3 x + 7 - 2}{x ^{3} - 1})

\frac{1}{36}

Decimal

0.02777 \dots

Solution steps

x \to 1 lim (\frac{3 x + 7 - 2}{x ^{3} - 1})

Apply L'Hopital's Rule

: x \to 1 lim \frac{\frac{1}{3 ( x + 7 ) ^{\frac{2}{3}}}}{3 x ^{2}}

= x \to 1 lim \frac{\frac{1}{3 ( x + 7 ) ^{\frac{2}{3}}}}{3 x ^{2}}

Plug in the value

x = 1

= \frac{\frac{1}{3 ( 1 + 7 ) ^{\frac{2}{3}}}}{3 \cdot 1 ^{2}}

Simplify

\frac{\frac{1}{3 ( 1 + 7 ) ^{\frac{2}{3}}}}{3 \cdot 1 ^{2}} : \frac{1}{36}

= \frac{1}{36}

\int x + x d x

(\frac{6 x ^{2} - 5}{4 - x})^{3}

x \to 0 lim (\frac{x - 5}{x - 1})

y = (5)^{x}

x \to 0 - lim (x^{2} cos (\frac{1}{x}))

What is the limit as x approaches 1 of (\sqrt[3]{x+7}-2)/(x^3-1) ?
The limit as x approaches 1 of (\sqrt[3]{x+7}-2)/(x^3-1) is 1/36