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

The limit as x approaches 6 of ((1/x-1/6))/(x-6) is -1/36

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

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

- \frac{1}{36}

Decimal

- 0.02777 \dots

Solution steps

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

Simplify

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

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

Plug in the value

x = 6

= - \frac{1}{6 \cdot 6}

Simplify

= - \frac{1}{36}

What is the limit as x approaches 6 of ((1/x-1/6))/(x-6) ?
The limit as x approaches 6 of ((1/x-1/6))/(x-6) is -1/36