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

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

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

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

1

Solution steps

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

Apply exponent rules

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

Apply the Limit Chain Rule:

1

= 1

\frac{1}{x + 9}

\frac{d}{d x} (arccos (arcsin (t)))

\frac{d}{d s} (\frac{3 s ^{3} + 19 s ^{2} + 41 s + 26}{( s + 1 )})

\frac{\partial}{\partial x} (x sin (\frac{8}{x}))

x \to 0 lim (cos^{2} (x) \cdot x)

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