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

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

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

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

- 1

Solution steps

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

Simplify

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

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

Plug in the value

x = 1

= - \frac{1}{1}

Simplify

= - 1

y = \frac{6}{x ^{4}}

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\frac{d ^{6}}{d x ^{6}} (1 - x^{2})

\int \frac{27}{1 + 9 x ^{2}} d x

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