TS EAMCET · Maths · Limits
If \(a>0, \lim _{x \rightarrow a} \frac{a^x-x^a}{x^x-a^a}=-1\), then \(a\) is equal to
- A 0
- B 1
- C \(e\)
- D \(2 e\)
Answer & Solution
Correct Answer
(B) 1
Step-by-step Solution
Detailed explanation
We have, \(\lim _{x \rightarrow a} \frac{a^x-x^a}{x^x-a^a}=-1\) Using \(L^{\prime}\) hospital's rule \(\Rightarrow \quad \lim _{x \rightarrow a} \frac{a^x \log a-a x^{a-1}}{x^x(1+\log x)}=-1\) \(\Rightarrow \quad \frac{a^a \log a-a \cdot a^{a-1}}{a^a(1+\log a)}=-1\)…
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