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

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

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

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

\frac{1}{2}

Decimal

0.5

Solution steps

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

Apply L'Hopital's Rule

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

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

Plug in the value

x = 3

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

Simplify

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

= \frac{1}{2}

y = 6 - 6 x, y = 0, x = 0

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

x \to - 3 lim (2 x + ∣ x - 3 ∣)

\int csc^{4} (3 x) d x

\int \frac{x}{1 - x ^{2}} d x

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