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

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

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

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

\infty

Solution steps

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

Simplify

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

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

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

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

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

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

= 1 \cdot \infty

Apply Infinity Property:

c \cdot \infty = \infty

= \infty

\int 2 cos (y^{2}) d y

e^{x + y} d x + e^{x - y} d y = 0

f (x) = \frac{x ^{2}}{x + 7}

f (x) = \frac{3 x ^{2}}{ln ( x )}

\int \frac{x ^{3}}{( 6 - x ^{4} ) ^{2}} d x

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