MCQ
Which of the following functions is decreasing on $\Big(0,\frac{\pi}{2}\Big)?$
- A$\sin2\text{x}$
- B$\tan\text{x}$
- C$\cos\text{x}$
- D$\cos3\text{x}$
Solution:
$\text{f}_1(\text{x})=\sin2\text{x},$ increases from '0' to '1' in $\Big(0,\frac{\pi}{2}\Big)$
$\text{f}_2(\text{x})=\tan\text{x}$ is increasing function in each quadrant.
$\text{f}_3(\text{x})=\cos\text{x},$ decreases from '1' to '0' in $\Big(0,\frac{\pi}{2}\Big) $
$ \text{f}_4(\text{x})=\cos3\text{x},$ decreases if $3\text{x}\in\Big(0,\frac{\pi}{2}\Big)\ \text{or x }\in\Big(0,\frac{\pi}{6}\Big)$
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$\vec{\text{a}}+\vec{\text{b}}$
$\vec{\text{a}}-\vec{\text{b}}$
$\vec{\text{b}}-\vec{\text{a}}$
$-\big(\vec{\text{a}}+\vec{\text{b}}\big)$