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

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

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

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

\infty

Solution steps

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

Divide by highest denominator power:

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

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

For

x

approaching

1

from the left

, x < 1 \Rightarrow \frac{1}{x} - 1 > 0

The denominator is a positive quantity approaching 0 from the right

= \infty

x \to 3 - lim (\frac{5 x}{x - 3})

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

x \to a lim (3 x^{2} + 4 x - 5)

x \to - \frac{π}{2} + lim (cos (x))

x \to \infty lim (\frac{10 - 6 x ^{2}}{5 + 3 e ^{x}})

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