Question

If $f\left(x\right),g\left(x\right)$ be differentiable functions and $f\left(1\right)=g\left(1\right)=2$ then $\underset{x\to 1}{lim}\frac{f\left(1\right)g\left(x\right)-f\left(x\right)g\left(1\right)-f\left(1\right)+g\left(1\right)}{g\left(x\right)-f\left(x\right)}$ is equal to

• A. $0$
• B. $1$
• C. $2$
• D. None of these

Answer 1

Answer: (C)

$2$

Limit $=\underset{x\to 1}{lim}\frac{f\left(1\right)g^{\prime }\left(x\right)-f^{\prime }\left(x\right)g\left(1\right)}{g^{\prime }\left(x\right)-f^{\prime }\left(x\right)}$

$=\underset{x\to 1}{lim}\frac{2[g^{\prime }\left(x\right)-f^{\prime }\left(x\right)]}{g^{\prime }\left(x\right)-f^{\prime }\left(x\right)}=\underset{x\to 1}{lim}2=2.$