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

\int x arccos (x) d x

in v erse l a pl a ce \frac{1}{s ^{2} + 2 s + 3}

\int_{2}^{9} \frac{1}{7 ( x - 2 ) ^{3}} d x

x \to - 7 - lim (\frac{1}{x ^{2} ( x + 7 )})

\frac{\partial}{\partial x} (\frac{x}{( x - 1 ) ^{2} + y ^{2}})

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