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

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

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

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

1

Solution steps

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

Simplify

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

= x \to 1 lim (x)

Plug in the value

x = 1

= 1

x \to 0 lim (x - e^{x} + 1)

x \to - 2 lim (\frac{1}{4 - x ^{2}})

x \to 4 lim (\frac{3 x ^{2} - 17 x + 20}{4 x ^{2} - 25 + 36})

x \to 0 + lim (\frac{e ^{- x}}{x})

x \to \infty lim (\frac{1.5 x}{3 x ^{2}})

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