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

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

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

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

\frac{1}{e}

Decimal

0.36787 \dots

Solution steps

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

Apply exponent rules

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

Apply the Limit Chain Rule:

\frac{1}{e}

= \frac{1}{e}

\frac{d}{d x} (\frac{sin ( x )}{tan ( x )})

x \to \frac{π}{5} - lim (cot (5 x))

\frac{d}{d x} (\frac{- 2 sin ( 2 x )}{13})

\int \frac{1}{8 ^{x}} d x

f (x) = 5 x^{2}, at x = 0

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