What is the limit as x approaches infinity of (1+7/x)^{2x} ?

The limit as x approaches infinity of (1+7/x)^{2x} is e^{14}

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limit as x approaches infinity of (1+7/x)^{2x}

x \to \infty lim ((1 + \frac{7}{x})^{2 x})

e^{14}

Decimal Notation

1202604.28416 \dots

Solution steps

x \to \infty lim ((1 + \frac{7}{x})^{2 x})

Apply exponent rules

= x \to \infty lim (e^{2 x l n (1 + \frac{7}{x})})

Apply the Limit Chain Rule:

e^{14}

= e^{14}

\frac{d}{d x} (x^{2} + \frac{2 a ^{3}}{x})

x \to + 3 - lim (\frac{3}{x ^{2} - 9})

y^{3} - (14 x + 8) + 3 x y^{2} y^{^{'}} = 0

x^{^{'}} = x

x \to 0 + lim (sin (x) ln (x))

What is the limit as x approaches infinity of (1+7/x)^{2x} ?
The limit as x approaches infinity of (1+7/x)^{2x} is e^{14}