Evaluate the following limit: `lim_(x->1)(1-1/x)/(sinpi(x-1))`

Explanation

`lim_(x->1)(1-1/x)/(s inpi(x-1))`

Take `x-1=y`

`=lim_(x-1->0)(x-1)/(xsin pi(x-1))`

`=lim_(y->0)(y)/(sin piy(y+1))`

`=lim_(y->0)(1)/(sin piy(y+1))`

`1/(lim_(y to 0)(y+1)xx lim_(y to 0)((sin pi y)/(y pi))pi)`

`=1/((1)(1xx pi))`

`=1/pi`