What is the limit as x approaches 7 of (1/x-1/7)/(x-7) ?

The limit as x approaches 7 of (1/x-1/7)/(x-7) is -1/49

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limit as x approaches 7 of (1/x-1/7)/(x-7)

x \to 7 lim (\frac{\frac{1}{x} - \frac{1}{7}}{x - 7})

- \frac{1}{49}

Decimal

- 0.02040 \dots

Solution steps

x \to 7 lim (\frac{\frac{1}{x} - \frac{1}{7}}{x - 7})

Simplify

\frac{\frac{1}{x} - \frac{1}{7}}{x - 7} : - \frac{1}{7 x}

= x \to 7 lim (- \frac{1}{7 x})

Plug in the value

x = 7

= - \frac{1}{7 \cdot 7}

Simplify

= - \frac{1}{49}

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What is the limit as x approaches 7 of (1/x-1/7)/(x-7) ?
The limit as x approaches 7 of (1/x-1/7)/(x-7) is -1/49