if f(x) has a derivative at x=a then lim x-->a [xf(a)-af(x)]/(x-a)=?

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Please find below the solution to the asked query:

fx has derivative at x=a i.e. fx is differentiable at x=aWe haveL=limxa xfa-afxx-aAt x=a, both numerator and denominator, become 0, hence it is 00 form.Hence L-Hopital rule can be applied.Differentiate numerator and denominator separately with respect to x.L=limxa fa-af'x1-0=limxa fa-a'fx=fa-a.f'a

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