ISI2019-MMA-5

Question

 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

• A. $-5$
• B. $-3$
• C. $3$
• D. $5$

Comments

I too got same answer.

Answer 1

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.