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

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

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

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

e

Decimal

2.71828 \dots

Solution steps

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

Apply exponent rules

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

Apply the Limit Chain Rule:

e

= e

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