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

Cem Hayes

Cem Hayes

Answered question

2021-02-25

Evaluate the following limits. limx0+xx2

Answer & Explanation

Ezra Herbert

Ezra Herbert

Skilled2021-02-26Added 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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