What is the limit as x approaches 0 of (1+x)^{5/x} ?

The limit as x approaches 0 of (1+x)^{5/x} is e^5

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limit as x approaches 0 of (1+x)^{5/x}

x \to 0 lim ((1 + x)^{\frac{5}{x}})

e^{5}

Decimal Notation

148.41315 \dots

Solution steps

x \to 0 lim ((1 + x)^{\frac{5}{x}})

Apply exponent rules

= x \to 0 lim (e^{\frac{5}{x} l n (1 + x)})

Apply the Limit Chain Rule:

e^{5}

= e^{5}

x^{2} \frac{d y}{d x} - 2 x y = 6 y^{4}, y (1) = \frac{1}{2}

f (x) = x^{2} + 33, at x = 4

\frac{\partial}{\partial x} (2 x + 4 y^{2})

\int (x + 1) (x - 1) d x

\int \frac{x ^{2} - 5 x + 1}{3 x ^{2}} d x

What is the limit as x approaches 0 of (1+x)^{5/x} ?
The limit as x approaches 0 of (1+x)^{5/x} is e^5