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

The limit as x approaches 0 of (1-3x)^{3/x} is 1/(e^9)

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

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

\frac{1}{e ^{9}}

Decimal Notation

0.00012 \dots

Solution steps

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

Apply exponent rules

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

Apply the Limit Chain Rule:

\frac{1}{e ^{9}}

= \frac{1}{e ^{9}}

\int_{0}^{2 π} sin^{2} (4 x) d x

y = \frac{6}{x}, (4, \frac{6}{2})

\int \frac{e ^{x}}{3} d x

\int \frac{6 - e ^{x}}{e ^{5 x}} d x

e^{x}, e^{- 4 x}, 0, ln (4)

What is the limit as x approaches 0 of (1-3x)^{3/x} ?
The limit as x approaches 0 of (1-3x)^{3/x} is 1/(e^9)