What is the limit as x approaches 0 of (1-6x)^{1/x} ?

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

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limit as x approaches 0 of (1-6x)^{1/x}

x \to 0 lim ((1 - 6 x)^{\frac{1}{x}})

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

Decimal Notation

0.00247 \dots

Solution steps

x \to 0 lim ((1 - 6 x)^{\frac{1}{x}})

Apply exponent rules

= x \to 0 lim (e^{\frac{1}{x} l n (1 - 6 x)})

Apply the Limit Chain Rule:

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

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

f (x) = 4 sec (x), at x = \frac{π}{3}

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

\frac{d}{d x} (tan (3 x^{4}))

(sec (x) tan (x))^{^{'}}

\frac{3 ( 7 x ^{2} - 2 x + 6 )}{4 x ^{\frac{5}{2}}}

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