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

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

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

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

1

Solution steps

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

Apply exponent rules

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

Apply the Limit Chain Rule:

1

= 1

x \to 0 + lim (\frac{2}{sin ( x )})

x \to 0 lim (\frac{- sin ( x )}{x})

x \to 0 lim (\frac{b ^{x} - a ^{x}}{x})

x \to \frac{5}{2} lim (\frac{4 x ^{2} - 25}{2 x - 5})

x \to 0 lim (\frac{( 8 + x ) ^{\frac{1}{3}} - 2}{x})

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