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  • The graph of the function has a unique tangent at the point (a, 0) through which

The graph of the function \mathrm{y=f(x)} has a unique tangent at the point (a, 0) through which the graph passes. Then \mathrm{\lim _{x \rightarrow a} \frac{\log _{\mathcal{c}}\{1+6 f(x)\}}{3 f(x)}} is

Option: 1

1


Option: 2

0


Option: 3

2


Option: 4

None of these


Answers (1)

best_answer

From the question, \mathrm{f(a)=0 \; and \; f(x)} is differentiable at x=a.
 

\mathrm{\therefore \quad \operatorname{limit}=\lim _{x \rightarrow a} \frac{\frac{1}{1+6 f(x)} \cdot 6 f^{\prime}(x)}{3 f^{\prime}(x)}=2 \cdot \frac{1}{1+6 f(a)}=2 .}

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Nehul

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