What is the limit as x approaches 1-of 1/(1-e^{x-1)} ?

The limit as x approaches 1-of 1/(1-e^{x-1)} is infinity

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limit as x approaches 1-of 1/(1-e^{x-1)}

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

\infty

Solution steps

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

For

x

approaching

1

from the left

, x < 1 \Rightarrow 1 - e^{x - 1} > 0

The denominator is a positive quantity approaching 0 from the right

= \infty

t \to - \infty lim (t^{3} e^{t})

x \to 4 + lim (\frac{4 - x}{4 - x})

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

x \to 0 lim (\frac{8 ^{x} - 3 ^{x}}{x})

x \to 0 lim (1 - \frac{3}{x}^{x})

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