Grade 12Integral Calculus
Check the monotonicity of f(x)=x÷sinx in (0,p÷2)
2 Answers
Sher Mohammad
f'(x)=sinx+xcosx/(sinx)^2=1/sinx(x)+xcos(x)/(sinx)^2f'(x)>0 for all x in 0 to p/4hence function in monotonically increasing.Sher MohammadB.Tech, IIT Delhi
Sher Mohammad
f'(x)=sinx-xcosx/(sinx)^2
for small x, sinx=x
f'(x)=x(1-cos x)> greater than zero
for higher values of x, also f'(x)>0, hence the function f(x) is monotonically increasing.
Sher Mohammad
B.Tech, IIT Delhi
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