Evaluate the following limits. lim_{xrightarrow0^+}x^{x^2}

Cem Hayes 2021-02-25 Answered
Evaluate the following limits. limx0+xx2
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Expert Answer

Ezra Herbert
Answered 2021-02-26 Author has 99 answers

We have given:
limx0+xx2
By the exponent rule ax=eln(ax)=exlna
limx0+xx2=limx0+ex2ln(x)
By the chain rule,
limx>0+xx2=limx0+ex2x
limx0+xx2=limx0+ex2+2x2ex2
limx0+xx2=e0+0
limx0+xx2=1+0
limx0+xx2=1
Result: 1

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