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 Notation

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

x^{3} y^{^{'''}} - x^{2} y^{^{''}} + 2 x y^{^{'}} - 2 y = 0

x \to - \infty lim (e^{3 x} (2 - x))

\int \frac{x x + x}{x ^{2}} d x

\int (\frac{3}{x} + \frac{5}{x ^{2}}) d x

3 sin (5 t + 45)

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