Grade Upto college level Differential Calculus
f(X)= x÷sinx in (0,p÷2) check the monotonicity?
1 Answer
bharat bajaj
Approved Tutor Answer12 Years agof(x)= x/sinx
df/dx = (sinx - xcosx)/ (sinx)^2
A function is monotonic if it is either increasing or decreasing in the given range.
Hence, check the sign of df/dx.
Hence, check the sign of df/dx.
df/dx = (tanx - x)cosx/(sinx)^2
tan x - x> 0 for (0,pi/2) . You may check it by making the graph.
cosx>0 for (0,pi2)
Hence, df/dx>0 for(0,pi/2)
cosx>0 for (0,pi2)
Hence, df/dx>0 for(0,pi/2)
Hence, this function is monotonic in the given range.
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