What is the limit as x approaches infinity of (1-1/(4x))^{8x} ?

The limit as x approaches infinity of (1-1/(4x))^{8x} is 1/(e^2)

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limit as x approaches infinity of (1-1/(4x))^{8x}

x \to \infty lim ((1 - \frac{1}{4 x})^{8 x})

\frac{1}{e ^{2}}

Decimal Notation

0.13533 \dots

Solution steps

x \to \infty lim ((1 - \frac{1}{4 x})^{8 x})

Apply exponent rules

= x \to \infty lim (e^{8 x l n (1 - \frac{1}{4 x})})

Apply the Limit Chain Rule:

\frac{1}{e ^{2}}

= \frac{1}{e ^{2}}

\int \frac{1}{x ^{2} e ^{\frac{1}{x}}} d x

\int (5 x - 1) (3 x^{2} + 2) d x

\int e^{x^{3}} (12 x^{2}) d x

\frac{\partial}{\partial x} (x e^{- \frac{y}{x}})

f (t) = \frac{3}{5} e^{- t} - \frac{22}{5} e^{4 t}

What is the limit as x approaches infinity of (1-1/(4x))^{8x} ?
The limit as x approaches infinity of (1-1/(4x))^{8x} is 1/(e^2)