11is the ans e√asin√a/2
\lim_{x\rightarrow a}\frac{1}{(x-a)}\int_{\sqrt{a}}^{\sqrt{x}}(te^t sin t)dt a>0
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12 Answers
1I think something's wrong ... Sagnik ...
If the actual expr. is considered as f(x) ..
Then ... f'(a) is the expr. that u have derived .... It's not the value of f(a) .... !!!!
1l'hosp n leibnitz in both v hav to diff d numr n denominator so in both way v can gt d anz
1actually ,,really gud questiotn ,,combined use of l'hospital rule n leibnitz formula
23L = lim_{x\rightarrow a} \frac{\int_{\sqrt{a}}^{\sqrt{x}}{te^{t}sintdt}}{x-a}
using L Hospital
L = lim_{x\rightarrow a}\frac{1}{2\sqrt{x}}\sqrt{x}e^{\sqrt{x}}sin\sqrt{x}
L = \frac{1}{2}e^{\sqrt{a}}sin\sqrt{a}
