What is the limit as x approaches 0+of (1-3x)^{2/x} ?

The limit as x approaches 0+of (1-3x)^{2/x} is 1/(e^6)

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limit as x approaches 0+of (1-3x)^{2/x}

x \to 0 + lim ((1 - 3 x)^{\frac{2}{x}})

\frac{1}{e ^{6}}

Decimal Notation

0.00247 \dots

Solution steps

x \to 0 + lim ((1 - 3 x)^{\frac{2}{x}})

Apply exponent rules

= x \to 0 + lim (e^{\frac{2}{x} l n (1 - 3 x)})

Apply the Limit Chain Rule:

\frac{1}{e ^{6}}

= \frac{1}{e ^{6}}

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

x \to 3 lim (\frac{x + 1}{x - 3})

x \to 1 - lim (ln (x) ln (1 - x))

x \to 0 lim (x csc (2 x))

x \to \frac{π}{2} lim ((1 + cos (x))^{3 s e c (x)})

What is the limit as x approaches 0+of (1-3x)^{2/x} ?
The limit as x approaches 0+of (1-3x)^{2/x} is 1/(e^6)