What is the limit as x approaches 0-of x^2-6/x ?

The limit as x approaches 0-of x^2-6/x is infinity

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limit as x approaches 0-of x^2-6/x

x \to 0 - lim (x^{2} - \frac{6}{x})

\infty

Solution steps

x \to 0 - lim (x^{2} - \frac{6}{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^{2}) - x \to 0 - lim (\frac{6}{x})

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

x \to 0 - lim (\frac{6}{x}) = - \infty

= 0 - (- \infty)

Simplify

0 - (- \infty) : \infty

= \infty

x \to 0 lim (cot (11 x))

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

x \to 1 lim (3 x - 5)

x \to 2 lim (\frac{5 x - 2}{x - 2})

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

What is the limit as x approaches 0-of x^2-6/x ?
The limit as x approaches 0-of x^2-6/x is infinity