What is the limit as x approaches 0+of (x)^x ?

The limit as x approaches 0+of (x)^x is 1

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limit as x approaches 0+of (x)^x

x \to 0 + lim ((x)^{x})

1

Solution steps

x \to 0 + lim (x^{x})

Apply exponent rules

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

Apply the Limit Chain Rule:

1

= 1

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x \to 0 + lim (cos (x) - 1)

\int 2 sec (x) tan (x) d x

\int \frac{cot ^{2} ( 2 x )}{sec ( 2 x )} d x

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