Question

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

• A. 0
• B. 1
• C. 2
• D. $\infty$

Answer 1

The correct option is C 2

$\underset{x\to a}{lim}\frac{\log [1+6f(x\left)\right]}{3f\left(x\right)}$

Multiplying and dividing by 2 we get,
$=2\cdot \underset{x\to a}{lim}\frac{\log [1+6f(x\left)\right]}{6f\left(x\right)}=2\times 1=2$ ----$(\underset{x\to a}{lim}\frac{\log [1+f(x\left)\right]}{f\left(x\right)}=1)$

since $\underset{x\to a}{lim}f\left(x\right)=2$