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

1 Answer
Mar 24, 2016

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.