What is the limit as x approaches 0 of (1-5x)^{3/x} ?

The limit as x approaches 0 of (1-5x)^{3/x} is 1/(e^{15)}

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limit as x approaches 0 of (1-5x)^{3/x}

x \to 0 lim ((1 - 5 x)^{\frac{3}{x}})

\frac{1}{e ^{15}}

Decimal Notation

3.05902 E - 7

Solution steps

x \to 0 lim ((1 - 5 x)^{\frac{3}{x}})

Apply exponent rules

= x \to 0 lim (e^{\frac{3}{x} l n (1 - 5 x)})

Apply the Limit Chain Rule:

\frac{1}{e ^{15}}

= \frac{1}{e ^{15}}

x^{3} csc (x)

\frac{d}{d x} (ln ((ln (x))^{2}))

\int \frac{1 - sin ^{3} ( x )}{sin ^{2} ( x )} d x

\frac{d}{d x} (\frac{2 x ^{2} - 3 x + 1}{x})

x^{2} + x y + 2 y^{2} = 28, (2, 3)

What is the limit as x approaches 0 of (1-5x)^{3/x} ?
The limit as x approaches 0 of (1-5x)^{3/x} is 1/(e^{15)}