Question:medium

If $f(x) = \begin{cases} \frac{9^x - 2 \cdot 3^x + 1}{\log(1+3x) \cdot \tan 2x} & , \text{if } x \neq 0 \\ a(\log b)^c & , \text{if } x = 0 \end{cases}$ is continuous at $x = 0$, then $a+b+c =$

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Standard Limits: $\lim_{x\to 0} \frac{a^x-1}{x} = \log a$; $\lim_{x\to 0} \frac{\log(1+x)}{x} = 1$; $\lim_{x\to 0} \frac{\tan x}{x} = 1$.
Updated On: Apr 30, 2026
  • $\frac{31}{6}$
  • $\frac{1}{6}$
  • $\frac{5}{6}$
  • $\frac{3}{20}$
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The Correct Option is A

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