What is the limit as x approaches 2 of (x-1)/(x^3-3) ?

The limit as x approaches 2 of (x-1)/(x^3-3) is 1/5

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limit as x approaches 2 of (x-1)/(x^3-3)

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

\frac{1}{5}

Decimal

0.2

Solution steps

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

Plug in the value

x = 2

= \frac{2 - 1}{2 ^{3} - 3}

Simplify

= \frac{1}{5}

x \to 0 lim (\frac{3 x ^{4} + 2 x ^{2}}{x ^{4} - x ^{2}})

x \to 0 lim (8 x csc (9 x))

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

x \to 0 lim (\frac{\frac{2}{3} cos ( x ) - 1}{x})

x \to 0 lim (\frac{e ^{x} - 1}{5 x ^{2}})

What is the limit as x approaches 2 of (x-1)/(x^3-3) ?
The limit as x approaches 2 of (x-1)/(x^3-3) is 1/5