Evaluate the following limit: `lim_(x->1)(1+cospix)/((1-x)^2)`

Explanation

`lim_(x->1)(1+cospix)/((1-x)^2)`

Take `x-1=y`

Then

`=lim_(y->0)(1+cospi(y+1))/(-y^2)`

`=lim_(y->0)(1+cospi(y+1))/(y^2)`

`=lim_(y->0)(1-cos piy)/(y^2)`

`=lim_(y->0)(2sin^2( piy)/2)/(y^2)`

`=2lim_(y->0)((sin( piy)/2)/((pi y)/2))^2 xx (pi^2)/4`

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