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})

x \to a lim [c \cdot f (x)] = c \cdot x \to a lim f (x)

= - 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

x \to 0 lim ((2 x + 1)^{2})

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

x \to - 3 - lim (9 - x^{2})

x \to - 2 lim (\frac{x ^{2} - x - 6}{x - 2})

x \to 0 + lim (x ln (x^{2} + x))

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