Question

If $f(0)=0=g(0)$ and $f^{\prime }(0)=6=g^{\prime }(0)$, then ${\lim }_{x\to 0}\frac{f(x)}{g(x)}$ is given by

• A. 1
• B. 0
• C. 12
• D. -1

Answer 1

Answer: (A)

${\lim }_{x\to 0}\frac{f\left(x\right)}{g\left(x\right)}={\lim }_{x\to 0}\frac{f^{\prime }\left(0\right)}{g^{\prime }\left(0\right)}$ (By L’ Hospital rule)
$=\frac{6}{6}=1$