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

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

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

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

1

Solution steps

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

Plug in the value

x = 1

= 1^{l n (1)}

Simplify

= 1

x \to 2 lim (\frac{sin ( π x )}{x ^{2} - 4})

x \to - \infty lim (\frac{4 x ^{2} + 1}{3 x - 1})

x \to 2 - lim (e^{\frac{1}{( x - 2 )}})

x \to 3 + lim (\frac{1 - x}{x - 3})

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

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