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[ If 0ltxlt(pi)/(2) then 1) (2)/(pi)gt(...

[ 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`

Text Solution

Verified by Experts

The correct Answer is:
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)`
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OBJECTIVE RD SHARMA ENGLISH-INCREASING AND DECREASING FUNCTIONS-Section I - Solved Mcqs
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  3. [ If 0ltxlt(pi)/(2) then 1) (2)/(pi)gt(sin x)/(x) (2)(pi)lt(sin x)/(...

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