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

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

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

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

1

Solution steps

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

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

x \to 1 - lim (1) = 1

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

= 1 - 0

Simplify

= 1

\int \frac{1}{17 - x ^{2}} d x

x e^{x}

\frac{d}{d x} ((ln (x^{5}))^{2})

f (x) = \frac{20}{3} x^{3} + 380 x^{2}

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