What is the limit as x approaches 0 of (1-6x)^{5/x} ?

The limit as x approaches 0 of (1-6x)^{5/x} is 1/(e^{30)}

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limit as x approaches 0 of (1-6x)^{5/x}

x \to 0 lim ((1 - 6 x)^{\frac{5}{x}})

\frac{1}{e ^{30}}

Decimal

9.35762 E - 14

Solution steps

x \to 0 lim ((1 - 6 x)^{\frac{5}{x}})

Apply exponent rules

= x \to 0 lim (e^{\frac{5}{x} l n (1 - 6 x)})

Apply the Limit Chain Rule:

\frac{1}{e ^{30}}

= \frac{1}{e ^{30}}

\frac{d y}{d x} - sin (x) y = 2 sin (x)

d er i v a t i v e g (t) = 5 (cos (π t))^{2}

\frac{d y}{d x} = 2 x - 1 + 2 x y - y

s l o p e (- 19.7, 10.5), (- 18.9, 3.4)

\frac{d}{d x} (cos (2 π x))

What is the limit as x approaches 0 of (1-6x)^{5/x} ?
The limit as x approaches 0 of (1-6x)^{5/x} is 1/(e^{30)}