What is the limit as x approaches infinity of (1+(2/x))^{(x/4)} ?

The limit as x approaches infinity of (1+(2/x))^{(x/4)} is sqrt(e)

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limit as x approaches infinity of (1+(2/x))^{(x/4)}

x \to \infty lim ((1 + (\frac{2}{x}))^{(\frac{x}{4})})

e

Decimal

1.64872 \dots

Solution steps

x \to \infty lim ((1 + \frac{2}{x})^{\frac{x}{4}})

Apply exponent rules

= x \to \infty lim (e^{\frac{x}{4} l n (1 + \frac{2}{x})})

Apply the Limit Chain Rule:

e

= e

\int_{0}^{3} x^{3} - 5 x d x

\frac{d y}{d x} = \frac{1}{7} y cos^{2} (y)

(y sin (x) + x y cos (x)) d x + (x sin (x) + 1) d y = 0

x \to 0 lim (\frac{x}{e ^{x}})

n \to \infty lim (ln (n))

What is the limit as x approaches infinity of (1+(2/x))^{(x/4)} ?
The limit as x approaches infinity of (1+(2/x))^{(x/4)} is sqrt(e)