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}}

\int \frac{1}{( x ^{2} - 4 x + 5 ) ^{2}} d x

f (x) = 3 x^{2} + x - 2, at x = 1

\int \frac{x - 2}{x ^{2} - x + 1} d x

\frac{\partial}{\partial x} (7 e^{x y} ln (x^{2} + y^{2}))

\frac{d}{d x} (x^{- \frac{5}{3}})

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)