TS EAMCET · Maths · Continuity and Differentiability
If \(f(x)=\left\{\begin{array}{ll}k, & \text { for } x=1 \ \frac{(9 x-1)(\sqrt{x}-1)}{3 x^2+2 x-5}, & \text { for } x \neq 1\end{array}\right.\) is continuous on \([0, \infty)\), then \(k=\)
- A \(\frac{1}{16}\)
- B \(\frac{1}{8}\)
- C \(\frac{1}{4}\)
- D \(\frac{1}{2}\)
Answer & Solution
Correct Answer
(D) \(\frac{1}{2}\)
Step-by-step Solution
Detailed explanation
We have, \(f(x)\) is continuous at \(x=1\) \(\therefore \quad k=\lim _{x \rightarrow 1} \frac{(9 x-1)(\sqrt{x}-1)}{3 x^2+2 x-5}\)…
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