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

The limit as x approaches infinity of ((1+1)/x)^{2x} is 0

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

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

0

Solution steps

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

Simplify

= x \to \infty lim ((\frac{2}{x})^{2 x})

Apply exponent rules

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

Apply the Limit Chain Rule:

0

= 0

What is the limit as x approaches infinity of ((1+1)/x)^{2x} ?
The limit as x approaches infinity of ((1+1)/x)^{2x} is 0