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

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

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

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

\infty

Solution steps

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

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

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

= 0 - (- \infty)

Simplify

0 - (- \infty) : \infty

= \infty

y^{^{'''}} + 6 y^{^{''}} + 45 y^{^{'}} = 0

y - x + x y^{^{'}} = 0

\int_{3}^{x^{3}} t^{4} d t

\int_{0}^{2} 2 x - x^{2} d x

\frac{\partial}{\partial y} (\frac{( 2 x + y )}{z})

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