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

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

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limit as x approaches 0-of x^3-1/x

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

\infty

Solution steps

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

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

With the exception of indeterminate form

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

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

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

= 0 - (- \infty)

Simplify

0 - (- \infty) : \infty

= \infty

x \to - 1 lim (ln (x + 2))

x \to \infty lim (e^{k x})

n \to \infty lim (\frac{cos ( n )}{n ^{2}})

x \to π lim (tan (\frac{x}{4}))

x \to 0 lim (x tan (\frac{π}{2} - x))

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