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

x \to + 0 lim (x \cdot ln (2 x))

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

x \to 1 lim (\frac{10 - x - 8 + x}{x ^{3} - 1})

x \to - 3 + lim (- \frac{sin ( c - 3 x )}{e ^{5 x + 15} - 1})

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

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