Tangent Line - Calc

Hello IronDome!

Does f(x) = sin1/x have a tangent line at x=0. Explain why or why not.

You mean f(x) = sin (1/x) ?

f(x) = sin (1/x) = sin (x ^-1)

f'(x) = cos (1/x) * (- 1/x²)

There is no tangent.  1 / (x = 0) and (-1/(x=0)²) is not defined.

1/0 is not defined.

Greeting asinus :- )

   !

Thanks asinus, it is always nice to see you here :)