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}

\frac{d y}{d t} = - 3 (y - 4)

\int 5 z^{3} e^{z} d z

f (x) = 8 x^{3}, at x = \frac{1}{2}

arctan (cos (θ))

\frac{d y}{d x}, y = \frac{- 5 x}{5} + 3 x^{3} - \frac{4}{5 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