What is the limit as x approaches 0+of e^{x^x} ?

The limit as x approaches 0+of e^{x^x} is e

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limit as x approaches 0+of e^{x^x}

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

e

Decimal Notation

2.71828 \dots

Solution steps

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

Apply the Limit Chain Rule:

e

= e

x \to 0 lim ((1 + 6 x)^{\frac{1}{x}})

x \to 0 lim (\frac{2 x ^{2} + x}{5 x})

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

x \to 0 + lim (5 x ln (x))

x \to 0 lim (\frac{sin ( ω ) x}{x})

What is the limit as x approaches 0+of e^{x^x} ?
The limit as x approaches 0+of e^{x^x} is e