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

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

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

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

1

Solution steps

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

Apply exponent rules

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

Apply the Limit Chain Rule:

1

= 1

\int \frac{1 + sin ( x )}{x ^{3}} d x

\int_{0}^{9} π (x - 1)^{2} d x

y = 7 e^{x} cos (x), (0, 7)

4 t^{3} - t^{2}, t^{4} + 2 t^{2}, 1 \leq t \leq 3

\int_{0}^{\infty} t e^{- 3 t} d t

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