What is the limit as x approaches 1+of x^{9/(1-x)} ?

The limit as x approaches 1+of x^{9/(1-x)} is 1/(e^9)

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limit as x approaches 1+of x^{9/(1-x)}

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

\frac{1}{e ^{9}}

Decimal

0.00012 \dots

Solution steps

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

Apply exponent rules

= x \to 1 + lim (e^{\frac{9}{1 - x} l n (x)})

Apply the Limit Chain Rule:

\frac{1}{e ^{9}}

= \frac{1}{e ^{9}}

d er i v a t i v e 2 sin (3 π x)

y^{^{'}} + \frac{2}{x} y = x, y (1) = 0

t an g e n t y = e^{x}

p a r i t y x \cdot tan (x)

l a pl a ce t r an s f or m t \cdot cos (t)

What is the limit as x approaches 1+of x^{9/(1-x)} ?
The limit as x approaches 1+of x^{9/(1-x)} is 1/(e^9)