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

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

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

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

e

Decimal

2.71828 \dots

Solution steps

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

Apply the common limit:

t \to 0 lim ((1 + t)^{\frac{1}{t}}) = e

= e

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