TS EAMCET · Maths · Continuity and Differentiability
If \(f(x)=\left\{\begin{array}{c}x^2\left|\cos \frac{\pi}{x}\right|, x \neq 0 \\ 0, x=0\end{array}\right.\), then at \(x=2, f(x)\) is
- A Differentiable
- B Continuous but not differentiable
- C Right differentiable only
- D Left differentiable only
Answer & Solution
Correct Answer
(B) Continuous but not differentiable
Step-by-step Solution
Detailed explanation
\(f(2) = 2^2 \left|\cos \frac{\pi}{2}\right| = 4 \cdot 0 = 0\) \(\lim_{x \to 2} f(x) = \lim_{x \to 2} x^2 \left|\cos \frac{\pi}{x}\right| = 2^2 \left|\cos \frac{\pi}{2}\right| = 0\) \(\lim_{x \to 2} f(x) = f(2) \implies f(x)\) is continuous at \(x=2\).…
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