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

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

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

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

e^{2 c}

Solution steps

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

Apply exponent rules

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

Apply the Limit Chain Rule:

e^{2 c}

= e^{2 c}

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x \to 1 lim (x^{4} e^{- x^{2}})

\frac{d}{d x} (- 2 x e^{- x})

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\frac{d}{d x} (x^{4} - 4 x)

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