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

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

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

t \to 1 lim (t^{\frac{1}{t - 1}})

e

Decimal

2.71828 \dots

Solution steps

t \to 1 lim (t^{\frac{1}{t - 1}})

Apply exponent rules

= t \to 1 lim (e^{\frac{1}{t - 1} l n (t)})

Apply the Limit Chain Rule:

e

= e

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