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

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

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

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

1 + \frac{1}{e}

Decimal Notation

1.36787 \dots

Solution steps

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

x \to 1 lim (1) = 1

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

= 1 + \frac{1}{e}

h \to 0 lim (\frac{\frac{2}{8 + h} - 8}{h})

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

x \to 0 lim (a^{m x})

h \to 0 lim (\frac{1 - cos ( h )}{h})

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

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