What is the limit as x approaches infinity of (1+5/x)^{x/7} ?

The limit as x approaches infinity of (1+5/x)^{x/7} is e^{5/7}

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limit as x approaches infinity of (1+5/x)^{x/7}

x \to \infty lim ((1 + \frac{5}{x})^{\frac{x}{7}})

e^{\frac{5}{7}}

Decimal Notation

2.04272 \dots

Solution steps

x \to \infty lim ((1 + \frac{5}{x})^{\frac{x}{7}})

Apply exponent rules

= x \to \infty lim (e^{\frac{x}{7} l n (1 + \frac{5}{x})})

Apply the Limit Chain Rule:

e^{\frac{5}{7}}

= e^{\frac{5}{7}}

\int \frac{2000}{5 x + 10} d x

\int_{0}^{2} x 5 - x^{2} d x

\frac{( s + 2 )}{( s ^{2} + s + 1 )}

\frac{- 25}{s ^{2} + 6 s + 25}

f (x) = x^{2} - 8, at x = 4

What is the limit as x approaches infinity of (1+5/x)^{x/7} ?
The limit as x approaches infinity of (1+5/x)^{x/7} is e^{5/7}