Question

[ If `0ltxlt(pi)/(2)` then 1) `(2)/(pi)gt(sin x)/(x) ` (2)`(pi)lt(sin x)/(x)` 3) `(sin x)/(x)gt1`, 4) `2lt(sin x)/(x)`
A. `2/pi lt (sin x)/(x)`
B. `(sin x)/(x) lt 1`
C. `(sin x)/(x) gt 1`
D. `(sin x)/(x) gt 1`

Answer 1

Correct Answer - B::C
In exmaple 36, we have shown that `f(x)=(sin x )/(x) "is decreasing on" (0, pi //2)`
`therefore underset(x rarr 0^+)lim f(x) gt f(x) gt underset(x rarr pi//2^-) (sin x)/x "for all" x in (0, pi//2)`
`rArr 1 gt (sin x)/(x) 2/pi "for all " in (0,pi//2)`