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

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

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

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

1

Solution steps

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

Apply exponent rules

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

Apply the Limit Chain Rule:

1

= 1

\int sin (π t) d t

x \to \infty lim (\frac{x}{e})

\int cos^{3} (\frac{x}{20}) d x

y^{^{''}} - 4 y^{^{'}} = 0

\frac{x e ^{t}}{1 + x e ^{t}}

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