What is the limit as x approaches 1 of x^{4/(1-x)} ?

The limit as x approaches 1 of x^{4/(1-x)} is 1/(e^4)

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limit as x approaches 1 of x^{4/(1-x)}

x \to 1 lim (x^{\frac{4}{1 - x}})

\frac{1}{e ^{4}}

Decimal

0.01831 \dots

Solution steps

x \to 1 lim (x^{\frac{4}{1 - x}})

Apply exponent rules

= x \to 1 lim (e^{\frac{4}{1 - x} l n (x)})

Apply the Limit Chain Rule:

\frac{1}{e ^{4}}

= \frac{1}{e ^{4}}

\int - x^{2} + 25 d x

y^{^{''}} + 3 y^{^{'}} - 40 y = 0

\int \frac{- 2}{t + 1} d t

\frac{1200}{s ^{2} ( s + 10 ) ^{2}}

\frac{2 x ^{3} - 6}{x ^{4}}

What is the limit as x approaches 1 of x^{4/(1-x)} ?
The limit as x approaches 1 of x^{4/(1-x)} is 1/(e^4)