## Related questions with answers

Question

Use numerical evidence to conjecture the value of the limit if it exists. Check your answer with your Computer Algebra System (CAS). If you disagree, which one of you is correct? $\lim _{x \rightarrow 0^{+}} x^{\ln x}$

Solution

VerifiedStep 1

1 of 2$\textbf{Numerical evidence:}$ From the table we can see that when $x$ approaches to 0 from positive side the function value increases without any boundation. So, I conjecture that

$\boxed{\lim\limits_{x \to 0^+}x^{\ln x} \textcolor{#c34632}{\text{ does not exist}}}$

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