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

n \to \infty lim (4)

x \to 0 lim ((x + 4)^{2})

x \to 2 lim (23 + 7)

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

x \to 2 lim (3 x^{2} - 4 x + 1)

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