Tuesday 17 August 2021

The polynomial \(x^{4}+4 x+c=0\) has at least one real root if and only if \(\qquad\) (a) \(c<2;\)\(\qquad\) (b) \(c \leq 2;\)\(\qquad\) (c) \(3>c\)\(\qquad\) (d) \(c \leq 3.\)

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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...