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

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

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

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

- \infty

Solution steps

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

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

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

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

= - \infty - \infty

Apply Infinity Property:

- \infty - \infty = - \infty

= - \infty

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