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ISI2019-MMA-5

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 If $f(a)=2, \: f’(a) = 1, \: g(a) =-1$ and $g’(a) =2$, then the value of   

                                  $$\lim _{x\rightarrow a}\frac{g(x) f(a) – f(x) g(a)}{x-a}$$ is

  1. $-5$
  2. $-3$
  3. $3$
  4. $5$
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easy way apply L'Hospital's rule.(because it is $0/0$ form)

ans = $g'(a)*f(a)- f'(a) *g(a) = 5$

hard way : Add and subtract $f(a) * g(a)$ and apply first principles definition.
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