Why is the y-intercept of $\frac {\sin(x)}{x}$ 1?

Question

I recently came across this function: $f(x) = \frac {\sin(x)}{x}$, and I graphed it on desmos. Why is the $y$-intercept $= 1$ despite $\sin(0)$ being divided by zero?

Answer 1

$f$ is not defined at $x=0$ but it does have a limit when $x \to 0$. This limit is the one defining the derivative of sin at $x=0$, a milestone in calculus: $$ \lim_{x\to0} \frac {\sin(x)}{x} = 1 $$