What is the limit as x approaches 0 of (6/(x+6)-1)/x ?

The limit as x approaches 0 of (6/(x+6)-1)/x is -1/6

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limit as x approaches 0 of (6/(x+6)-1)/x

x \to 0 lim (\frac{\frac{6}{x + 6} - 1}{x})

- \frac{1}{6}

Decimal

- 0.16666 \dots

Solution steps

x \to 0 lim (\frac{\frac{6}{x + 6} - 1}{x})

Simplify

\frac{\frac{6}{x + 6} - 1}{x} : - \frac{1}{x + 6}

= x \to 0 lim (- \frac{1}{x + 6})

Plug in the value

x = 0

= - \frac{1}{0 + 6}

Simplify

= - \frac{1}{6}

What is the limit as x approaches 0 of (6/(x+6)-1)/x ?
The limit as x approaches 0 of (6/(x+6)-1)/x is -1/6