Question

What is the equation of the tangent line of `f(x)=(sinpi/x)/x` at `x=1`?

Answer 1

I think this is a trick or challenge question. What is `sinpi`?

Explanation:

`f(x) = (sinpi/x)/x = sinpi/x^2`.

But `sinpi = 0`, so `f(x) = 0` with restricted domain `x != 0`

The tangent line to a line at a point on the line is the line itself.

Therefore the tangent at `x = 1` is the horizontal line whose equation is `y=0`. (This horizontal line is also known as the `x`-axis.)

(Alternatively, `f'(x) = 0`, so `f'(1) = 0`, so the tangent line is horizontal.)