12. If function f (x) is differenti...
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12. If function f (x) is differentiable at x = a, then lim x'f(a)-a'f(x) x-a (2011) (a) 2a f(a) +af (a) (c) af(a)-a²f (a) (b) –a?f' (a) (d) 2af (a) – a f(a) i bar

JEE/Engineering Exams
Maths
Solution
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( lim _{x rightarrow infty} frac{x^{2} f(a)-a^{2} f(x)}{x-a} quad ) Appering thorpital rule [ begin{array}{l}lim _{x rightarrow a} frac{2 x f(a)-a^{2} f^{prime}(x)}{1-0} text { thy }=2 a f(a)-a^{2} f^{prime}(a)(d)end{array} ]
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