How do you graph y= x cos xy=xcosx?

1 Answer
A. S. Adikesavan
Mar 24, 2016

The graph is oscillatory between y = x and y=-xy=−x. The expanding waves meet x-axis at origin and x=+-(2n-1)pi/2x=±(2n−1)π2, n =1, 2, 3, 4, .

Explanation:

|y|=|x cos x|<=|x||y|=|xcosx|≤|x|

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

y = 0, when x = 0 and cos x =0.
cos(+-(2n-1)pi/2) = 0cos(±(2n−1)π2)=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+-oox→±∞ of x cos x are indeterminate.

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