MCQ
If A = {1, 3, 5, B} and B = {2, 4}, then:
- A$4\in\text{A}$
- B$\{4\}\subset\text{A}$
- C$\text{B}\subset\text{A}$
- ✓None of these.
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$\lim _{t \rightarrow x} \frac{f(x) \sin t-f(t) \sin x}{t-x}=\sin ^2 x \text { for all } x \in(0, \pi)$
If $f \left(\frac{\pi}{6}\right)=-\frac{\pi}{12}$, then which of the following statement(s) is (are) TRUE?
$(A)$ $f \left(\frac{\pi}{4}\right)=\frac{\pi}{4 \sqrt{2}}$
$(B)$ $f(x)<\frac{x^4}{6}-x^2$ for all $x \in(0, \pi)$
$(C)$ There exists $\alpha \in(0, \pi)$ such that $f ^{\prime}(\alpha)=0$
$(D)$ $f ^{\prime \prime}\left(\frac{\pi}{2}\right)+ f \left(\frac{\pi}{2}\right)=0$
