Question

The values of $f\left(x\right)=2\sin \sqrt{x^2+x+1}$lie in the interval __________ .

Answer 1

$$\begin{gathered} f\left(x\right)=2\sin \sqrt{x^2+x+1} \\ \mathrm{Since}-1\le \sin \theta \le 1 \\ \mathrm{i}.\mathrm{e}-1\le \sin \sqrt{x^2+x+1}\le 1 \\ \mathrm{i}.\mathrm{e}-2\le 2\sin \sqrt{x^2+x+1}\le 2 \\ \mathrm{i}.\mathrm{e}2\sin \sqrt{x^2+x+1}\in \left[-2,2\right] \\ \mathrm{i}.\mathrm{e}.2\sin \sqrt{x^2+x+1}\mathrm{lies}\mathrm{in}\mathrm{interval}\left[-2,2\right] \end{gathered}$$