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

x \to 3 - lim (\frac{1}{9 - x ^{2}})

x \to - 2 lim (\frac{x - 2}{4 - x ^{2}})

x \to 0 lim (2 x + 33)

x \to 0 lim ((2 x)^{3 x})

x \to 0 lim ((sin (\frac{1}{x})) x)

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