Question

`Lim x to 1` f(x)=`(tan(pix))/(pi(x-1))` ?

Answer 1

`1`

Explanation:

making `y = x-1` we have

`tan(pi(y+1))/(pi y)=tan(pi y)/(pi y) = sin(pi y)/(pi y) 1/cos(piy)`

Now `x->1 rArr y->0` then

`lim_( x->1)(tan(pix))/(pi(x-1)) equiv lim_(y->0)sin(pi y)/(pi y) 1/cos(piy)=lim_(y->0)sin(pi y)/(pi y) lim_(y->0)1/cos(piy) = 1 xx 1 = 1`