What is the limit as x approaches 0+of (1-2x)^{1/x} ?

The limit as x approaches 0+of (1-2x)^{1/x} is 1/(e^2)

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limit as x approaches 0+of (1-2x)^{1/x}

x \to 0 + lim ((1 - 2 x)^{\frac{1}{x}})

\frac{1}{e ^{2}}

Decimal

0.13533 \dots

Solution steps

x \to 0 + lim ((1 - 2 x)^{\frac{1}{x}})

Apply exponent rules

= x \to 0 + lim (e^{\frac{1}{x} l n (1 - 2 x)})

Apply the Limit Chain Rule:

\frac{1}{e ^{2}}

= \frac{1}{e ^{2}}

4 x^{2} + y = 4, x^{4} - y = 1

x \to \infty + lim (\frac{x ^{5} - 3 x ^{2} + 5 x - 9}{7 x ^{4} - 6 x ^{2} + 5 x - 9})

\frac{d}{d x} (e^{l n (3)})

y = x^{2} - 3 x + 3

\int \frac{1}{2 - 3 x - 4 x ^{2}} d x

What is the limit as x approaches 0+of (1-2x)^{1/x} ?
The limit as x approaches 0+of (1-2x)^{1/x} is 1/(e^2)