What is the limit as x approaches 0-of (x^2)/2-8/x ?

The limit as x approaches 0-of (x^2)/2-8/x is infinity

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limit as x approaches 0-of (x^2)/2-8/x

x \to 0 - lim (\frac{x ^{2}}{2} - \frac{8}{x})

\infty

Solution steps

x \to 0 - lim (\frac{x ^{2}}{2} - \frac{8}{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}}{2}) - x \to 0 - lim (\frac{8}{x})

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

x \to 0 - lim (\frac{8}{x}) = - \infty

= 0 - (- \infty)

Simplify

0 - (- \infty) : \infty

= \infty

x \to 2 lim (∣ x - 2 ∣)

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

x \to 1 lim (ln (7 x) + e^{x})

f (x) = 20 x

y = \frac{x ^{2}}{e ^{x}}

What is the limit as x approaches 0-of (x^2)/2-8/x ?
The limit as x approaches 0-of (x^2)/2-8/x is infinity