If `f(x)=(1-sinx)/((pi-2x)^2),w h e nx!=pi/2a n df(pi/2)=lambda,` the `f(x)` will be continuous function at `x=pi/2,w h e r elambda=` `1/8` (b) `1/4` (c) `1/2` (d) none of these

Options

A. `1//8`
B. `1//4`
C. `1//2`
D. none of these

Answer

A

Explanation

f(x) will be continous at `x=pi//2`, if
`underset(x to pi//2)lim=f(x)=f((pi)/(2))`
`Rightarrow underset(x to pi//2)lim f(x)=(1-sinx)/((pi-2x)^(2))=lambda`
`(1)/(4) underset(x to pi//2)lim (1-cosx(pi//2-x))/((pi//2-x^(2)))=lambda`
`Rightarrow (1)/(4)xx(1)/(2)=lambda" "[therefore underset(x to 0)lim (1-cos x)/(x)=(1)/(2)]`
`Rightarrow lambda=(1)/(8)`