Wednesday 31 January 2018


If the inequality \(\sin ^{2}x+a\cos x+a^{2}\geq1+\cos x\) holds for any \(x\in \textbf{R}\),then find the range of values for negative \(\textbf{a}\).
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Define \(f: \mathbb{R} \rightarrow \mathbb{R}\) by \[f(x)= \begin{cases}(1-\cos x) \sin \left(\frac{1}{x}\right), & x \neq 0 \\ 0, &a...