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

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

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

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

1

Solution steps

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

Apply exponent rules

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

Apply the Limit Chain Rule:

1

= 1

\frac{d}{d x} (x^{3} ln (7 x))

f (x) = e^{4 - 5 x} (3 x^{3} - 2)^{6}

y^{^{'}} = 2 x + y, y (0) = 9

y^{^{''}} - y = 10 sin^{2} (x)

\int 2^{x} (2^{- x} + 1) d x

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