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

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

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

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

- \infty

Solution steps

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

Simplify

\frac{1}{x} - \frac{1}{x ^{2}} : \frac{x - 1}{x ^{2}}

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

\frac{x - 1}{x ^{2}} = (x - 1) \frac{1}{x ^{2}}

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

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

With the exception of indeterminate form

= x \to 0 + lim (x - 1) \cdot x \to 0 + lim (\frac{1}{x ^{2}})

x \to 0 + lim (x - 1) = - 1

x \to 0 + lim (\frac{1}{x ^{2}}) = \infty

= (- 1) \cdot \infty

Apply Infinity Property:

- c \cdot \infty = - \infty

= - \infty

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