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

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

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

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

\infty

Solution steps

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

Divide by highest denominator power:

1 - \frac{1}{x}

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

x \to a lim [f (x) \pm g (x)] = x \to a lim f (x) \pm x \to a lim g (x)

With the exception of indeterminate form

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

x \to 0 - lim (1) = 1

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

= 1 - (- \infty)

Simplify

1 - (- \infty) : \infty

= \infty

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