Question

The graph of the function $y=f\left(x\right)$ has the unique tangent at the point $(a,0)$ through which the graph passes. Then $\underset{x\to a}{lim}\frac{{\log }_e\{1+6f\left(x\right)\}}{3f\left(x\right)}$ is

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

Answer 1

The correct option is C $2$

$f\left(a\right)=0$
And as $f\left(x\right)$ is differentialble at $x=a$
$\underset{x\to a}{lim}\frac{\frac{1}{1+6f\left(x\right)}.6f^{\prime }\left(x\right)}{3f^{\prime }\left(x\right)}=2.\frac{1}{1+6f\left(a\right)}=2$