A) is continuous on \[\left( 0,\frac{\pi }{2} \right)\]
B) is strictly increasing in \[\left( 0,\frac{\pi }{2} \right)\]
C) is strictly decreasing in \[\left( 0,\frac{\pi }{2} \right)\]
D) has global maximum value 2
Correct Answer: A
Solution :
For \[0<x\le \frac{\pi }{2};\] \[[\cos \,\,x]=0\] Hence, \[f(x)=1\]for all \[\left( 0,\frac{\pi }{2} \right]\] Trivially \[f(x)\] is continuous on \[\left( 0,\frac{\pi }{2} \right)\] This function is neither strictly increasing nor strictly decreasing and its global maximum is 1.
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