AP EAMCET · Maths · Continuity and Differentiability
If \(f(x)= \begin{cases}\frac{1-\sqrt{2} \sin x}{\pi-4 x} & \text { if } x \neq \frac{\pi}{4} \\ a & \text { if } x=\frac{\pi}{4}\end{cases}\) is continuous at \(\frac{\pi}{4}\), then \(a\) is equal to
- A 4
- B 2
- C 1
- D \(1 / 4\)
Answer & Solution
Correct Answer
(D) \(1 / 4\)
Step-by-step Solution
Detailed explanation
\(\because \quad f(x)= \begin{cases}\frac{1-\sqrt{2} \sin x}{\pi-4 x}, & \text { if } x \neq \frac{\pi}{4} \\ a, & \text { if } x=\frac{\pi}{4}\end{cases}\) \(\lim _{x \rightarrow \frac{\pi}{4}} f(x)=\lim _{x \rightarrow \frac{\pi}{4}} \frac{1-\sqrt{2} \sin x}{\pi-4 x}\)…
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