3. a) Show that the function given by f (x) = \sin x is  increasing in \left ( 0 , \pi /2 \right )

Answers (1)

Given f(x) = sinx
f^{'}(x) = \cos x
Since,     \cos x > 0 \ for \ each \ x\ \epsilon \left ( 0,\frac{\pi}{2} \right )
f^{'}(x) > 0
Hence, f(x) = sinx is strictly increasing in   \left ( 0,\frac{\pi}{2} \right )

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