TS EAMCET · Maths · Continuity and Differentiability
If the function \(f(x)= \begin{cases}\frac{\tan a(x-1)}{x-1}, & \text { if } 0 \lt x \lt 1 \ \frac{x^3-125}{x^2-25}, & \text { if } 1 \leq x \leq 4 \ \frac{b^x-1}{x}, & \text { if } x\gt4\end{cases}\) is continuous in its domain, then \(6 a+9 b^4=\)
- A 284
- B 261
- C 214
- D 317
Answer & Solution
Correct Answer
(A) 284
Step-by-step Solution
Detailed explanation
\left.\begin{array}{l}\text { } f(x)= \begin{cases}\frac{\tan a(x-1)}{x-1}, & \text { if } 0 \lt x \lt 1 \\ \frac{x^3-125}{x^2-25}, & \text { if } 1 \leq x \leq 4 \\ \frac{6^x-1}{x}, & \text { if } x\gt4\end{cases} \\ f(x) \text { is continuous. } \Rightarrow \lim _{x…
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