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 e^2

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

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

e^{2}

Decimal

7.38905 \dots

Solution steps

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

Apply exponent rules

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

Apply the Limit Chain Rule:

e^{2}

= e^{2}

\frac{9}{x + 2}

\int 3 x^{2} + 10 x - 5 d x

x \to - 2 - lim (- 3 x^{2} - 5 x + 3)

\int 10 csc^{2} (x) - sin (x) d x

(x^{2} + 1) \frac{d y}{d x} + 6 x (y - 1) = 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 e^2