Chapter 3.5, Problem 70E

Exploring $\left(\sin kx\right)/x$ Graph $y=\left(\sin x\right)/x$, $y=\left(\sin 2x\right)/x$, and $y=\left(\sin 4x\right)/x$ together over the interval $-2\le x\le 2$. Where does each graph appear to cross the y-axis? Do the graphs really intersect the axis? What would you expect the graphs of $y=\left(\sin 5x\right)/x$ and $y=\left(\sin \left(-3x\right)\right)/x$ to do as $x\to 0$? Why? What about the graph of $y=\left(\sin kx\right)/x$ for other values of $k$? Give reasons for your answers.