What is the limit as x approaches 0-of 2/x-1/(x^3) ?

The limit as x approaches 0-of 2/x-1/(x^3) is infinity

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limit as x approaches 0-of 2/x-1/(x^3)

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

\infty

Solution steps

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

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

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

x \to a lim [c \cdot f (x)] = c \cdot x \to a lim f (x)

= 2 \cdot x \to 0 - lim (\frac{1}{x} (1 - \frac{\frac{1}{x ^{3}}}{\frac{2}{x}}))

x \to a lim [f (x) \cdot g (x)] = x \to a lim f (x) \cdot x \to a lim g (x)

With the exception of indeterminate form

= 2 \cdot x \to 0 - lim (\frac{1}{x}) \cdot x \to 0 - lim (1 - \frac{\frac{1}{x ^{3}}}{\frac{2}{x}})

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

x \to 0 - lim (1 - \frac{\frac{1}{x ^{3}}}{\frac{2}{x}}) = - \infty

= 2 (- \infty) (- \infty)

Apply Infinity Property:

2 (- \infty) (- \infty) = \infty

= \infty

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

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

t \to 0 lim (\frac{2 sin ( t )}{t})

x \to 4 + lim (e^{\frac{2}{x}})

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

What is the limit as x approaches 0-of 2/x-1/(x^3) ?
The limit as x approaches 0-of 2/x-1/(x^3) is infinity