What is `underset(xrarr(pi)/(2))limf(x)=underset(xrarr(pi)/(2))lim(1-sinx)/((pi-2x)^(2))` equal to ?

Options

A. 1
B. `1//2`
C. `1//4`
D. `1//8`

Answer

D

Explanation

`underset(xto(pi)/(2))limf(x)=underset(xto(pi)/(2))lim(1-sinx)/((pi-2x)^(2))`
`=underset(xto(pi)/(2))lim(-cosx)/((pi-2x)(-2))`
`=underset(xto(pi)/(2))lim(cosx)/(4(pi-2x))`
and `=underset(xto(pi)/(2))lim(-sinx)/(4(-2))=underset(xto(pi)/(2))lim(sinx)/(8)`
`=(1)/(8).sin""(pi)/(2)=(1)/(8)xx1=(1)/(8)`