Question

`lim_(xrarr1)sin(π/(x-1))``=`?

`lim_(xrarr1)sin(π/(x-1))`

Answer 1

The limit does not exist.

Explanation:

As `x` approaches `1`, the argument, `pi/(x-1)` takes on values `pi/2 + 2pik` and `(3pi)/2 + 2pik` infinitely often.

So `sin(pi/(x-1))` takes on values `-1` and `1`, infinitely many times.

The value cannot be approaching a single limiting number.

graph{sin(pi/(x-1)) [-1.796, 8.07, -1.994, 2.94]}