Question

The value of x for which `f(x)=(sin.({x})/({x})+cos.({x})/({x}))` is maximum ({x} and [x] denots fractiona part and greatest integer part of x respectively)
A. `1+(pi)/(4)`
B. `2+(pi)/(4)`
C. `1-(pi)/(4)`
D. none of these

Answer 1

Correct Answer - A
Let `({x})/([x])=alpha`
`rArrf(x)= sin alpha + cos alpha`
`" " =sqrt(2)(sin((pi)/(4)+alpha))`
f(x) is maximum at `alpha(pi)/(4)`
`:. ({x})/([x])=(pi)/(4)`
`rArr {x}=(pi)/(4)[x]`
is true at [x]=1
`:. {x}=(pi)/(4)`
So `x=[x]+{x}=1+(pi)/(4)`