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

The limit as x approaches infinity of (1-2/x)^{8x} is 1/(e^{16)}

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

x \to \infty lim ((1 - \frac{2}{x})^{8 x})

\frac{1}{e ^{16}}

Decimal

1.12535 E - 7

Solution steps

x \to \infty lim ((1 - \frac{2}{x})^{8 x})

Apply exponent rules

= x \to \infty lim (e^{8 x l n (1 - \frac{2}{x})})

Apply the Limit Chain Rule:

\frac{1}{e ^{16}}

= \frac{1}{e ^{16}}

x \to 0 lim (x^{3} cot (x))

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

x \to - \infty lim (\frac{2 - 3 e ^{- x}}{5 e ^{- x} - 4})

x \to \infty lim (\frac{x}{e ^{- x}})

x \to 1 lim (\frac{π}{x - 1})

What is the limit as x approaches infinity of (1-2/x)^{8x} ?
The limit as x approaches infinity of (1-2/x)^{8x} is 1/(e^{16)}