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If lim(xto(pi)/(2)) (sinx)/(x)=l and lim...

If `lim_(xto(pi)/(2)) (sinx)/(x)=l and lim_(xtooo) (cosx)/(x)=m`, then which one of the following is correct?

A

`l=1,m=1`

B

`l=(2)/(pi),m=oo`

C

`l=(2)/(pi),m=0`

D

`l=1,m=oo`

Text Solution

Verified by Experts

The correct Answer is:
C
`underset(xto(pi)/(2))lim(sinx)/(x)=landunderset(xtooo)lim(cosx)/(x)=m`
`underset(xto(pi)/(2))lim(sinx)/(x)=(1)/(pi/2)=(2)/(pi),underset(xtooo)lim(cosx)/(x)=0`
`:.l=(2)/(pi),m=0`
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