What is the limit as x approaches 0 of (1-x)^{5/x} ?

The limit as x approaches 0 of (1-x)^{5/x} is 1/(e^5)

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limit as x approaches 0 of (1-x)^{5/x}

x \to 0 lim ((1 - x)^{\frac{5}{x}})

\frac{1}{e ^{5}}

Decimal

0.00673 \dots

Solution steps

x \to 0 lim ((1 - x)^{\frac{5}{x}})

Apply exponent rules

= x \to 0 lim (e^{\frac{5}{x} l n (1 - x)})

Apply the Limit Chain Rule:

\frac{1}{e ^{5}}

= \frac{1}{e ^{5}}

f (x) = sin^{2} (x^{2})

\int \frac{x ^{4} + x - 4}{x ^{2} + 2} d x

\frac{d}{d x} (\frac{x}{x ^{2} + 64})

\frac{d y}{d x} (x^{2}) = y^{3}

\int \frac{1}{3 t ^{2}} d t

What is the limit as x approaches 0 of (1-x)^{5/x} ?
The limit as x approaches 0 of (1-x)^{5/x} is 1/(e^5)