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If f(x)={1/((pi-2x)^2)dot(logsinx)/((lo...

If `f(x)={1/((pi-2x)^2)dot(logsinx)/((log(1+pi^2-4pix+4x^2)),x!=pi/2k ,x=pi/2` is continuous at `x=pi/2,t h e nk=` `-1/(16)` (b) `-1/(32)` (c) `-1/(64)` (d) `-1/(28)`

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`lim_(x->(pi)/2) (1-sinx)/(pi-2x)^2xx(logsinx)/log(1+pi^2-4pix+4x^2)`
`x=pi/2-h`
`lim_(h->0) (1-cosh)/(4h^2)xx(logcosh)/log(1+4h^2)`
`(1-cosh)/h^2=(2sin^2(h/2))/(h^2/2.2)`
`=2/4(sin^2(h/2))/(h/2)=1`
`=1/4xx1/2xx(log cosh)/(log(1+4h^2))`
`lim_(h->0) 1/8xx(log cosh)/(log (1+4h^2))`
`=(1/cosh)-sinh/(1/1+4h^2xx8h)`
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