What is the limit as x approaches 0 of \sqrt[x]{1+x} ?

The limit as x approaches 0 of \sqrt[x]{1+x} is e

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limit as x approaches 0 of \sqrt[x]{1+x}

e

Decimal Notation

2.71828 \dots

Solution steps

Apply the common limit:

= e

x \to - 1 lim (\frac{x + 5}{x + 1})

x \to 0 lim (4 x + 1)

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

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

x \to 0 lim (sin (x) csc (6 x))

What is the limit as x approaches 0 of \sqrt[x]{1+x} ?
The limit as x approaches 0 of \sqrt[x]{1+x} is e