What is the limit as x approaches 0+of (1-x)^{ln(x)} ?

The limit as x approaches 0+of (1-x)^{ln(x)} is 1

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limit as x approaches 0+of (1-x)^{ln(x)}

x \to 0 + lim ((1 - x)^{l n (x)})

1

Solution steps

x \to 0 + lim ((1 - x)^{l n (x)})

Apply exponent rules

= x \to 0 + lim (e^{l n (x) l n (1 - x)})

Apply the Limit Chain Rule:

1

= 1

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x \to - 5 - lim (\frac{4 x ^{2} - 12}{x + 5})

x \to \infty lim (- x^{2} + 1)

x \to 0 lim (\frac{x \cdot s h ( 2 x )}{c h ( 4 x ) - 1})

What is the limit as x approaches 0+of (1-x)^{ln(x)} ?
The limit as x approaches 0+of (1-x)^{ln(x)} is 1