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

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

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

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

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

Decimal

3.05902 E - 7

Solution steps

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

Apply exponent rules

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

Apply the Limit Chain Rule:

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

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

x \to 0 lim (x ln (1 + x))

x \to 0 lim (sin^{2} (x^{2}))

x \to 0 lim (4 x - 3)

x \to - 3 lim (\frac{6 x + 5}{x + 8})

x \to 1 + lim (x^{\frac{8}{x - 1}})

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