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  • If the graph of the continuous function y = f(x) passes through (a,0)  then   <img alt="\lim _{x \rightarrow

If the graph of the continuous function y = f(x) passes through (a,0)  then   \lim _{x \rightarrow a} \frac{\ln \left(1+6 f^2(x)-3 f(x)\right.}{3 f(x)}  is equal to: 

Option: 1

1


Option: 2

0


Option: 3

-1


Option: 4

none of these


Answers (1)

best_answer

Since  f(a)=0 \Rightarrow \lim _{x \rightarrow a}\left(6 f^2(x)-3 f(x)\right)=0

\lim _{x \rightarrow a} \frac{\ln \left(1+6 f^2(x)-3 f(x)\right)}{3 f(x)} =\lim _{x \rightarrow a} \frac{\ln \left(1+6 f^2(x)-3 f(x)\right)}{\left(6 f^2(x)-3 f(x)\right)} \cdot \frac{\left(6 f^2(x)-3 f(x)\right)}{3 f(x)} \\

=\lim _{x \rightarrow a} \frac{6 f(x)-3}{3}=-1

 

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Anam Khan

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