What is the limit as x approaches 0-of x| 1/x | ?

The limit as x approaches 0-of x| 1/x | is -1

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limit as x approaches 0-of x| 1/x |

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

- 1

Solution steps

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

\frac{1}{x}

is negative when

x \to 0 -

. Therefore

\frac{1}{x} = - \frac{1}{x}

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

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

= x \to 0 - lim (- 1)

x \to a lim c = c

= - 1

What is the limit as x approaches 0-of x| 1/x | ?
The limit as x approaches 0-of x| 1/x | is -1