Question

How do you graph `y= x cos x`?

Answer 1

The graph is oscillatory between y = x and `y=-x`. The expanding waves meet x-axis at origin and `x=+-(2n-1)pi/2`, n =1, 2, 3, 4, .

Explanation:

`|y|=|x cos x|<=|x|`

If (x, y) is on the graph, so is `(-x, -y)`. So, the graph is symmetrical about the origin.

y = 0, when x = 0 and cos x =0.
`cos(+-(2n-1)pi/2) = 0`, for n = 1, 2, 3, ...
So, the curve meets x-axis at (0, 0), (+-(2n-1)pi/2, 0)#, n= 1, 2, 3, ...

Limits `xto+-oo` of x cos x are indeterminate.