I have come across this question in one of my previous year question paper l tried solving it but I getting stuck in differentiating someone please help me out...
2026-04-07 05:21:47.1775539307
$\lim\limits_{x\to a}\left(\frac{x^x-a^x}{x^a-a^a}\right)$ using L'Hospital's rule.
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For $a>0$ use $$\frac{x^x-a^a}{x^a-a^a}=\frac{\frac{x^x-a^a}{x-a}-\frac{a^x-a^a}{x-a}}{\frac{x^a-a^a}{x-a}}$$ and a definition of a derivative.
By the L'Hospital we obtain the same result: $$\frac{a^a(\ln{a}+1)-a^a\ln{a}}{a\cdot a^{a-1}}=1.$$