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Check the monotonicity of f(x)=x÷sin x in (0,p÷2)

Check the monotonicity of f(x)=x÷sin x in (0,p÷2)

Grade:12th pass

1 Answers

Arun Kumar IIT Delhi
askIITians Faculty 256 Points
9 years ago
Hello Student,
f'(x)=sinx-xcosx/(sinx)^2
sinx=x for x <<1
f'(x)=x(1-cos x)> 0
=>f'(x)>0
=>f(x) is monotonically increasing

Thanks & Regards
Arun Kumar
Btech, IIT Delhi
Askiitians Faculty

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