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

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

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Answer 1 · 2016-03-24T17:38:13

The graph is oscillatory between y = x and $y = - x$ $y=-x$ . The expanding waves meet x-axis at origin and $x = \pm (2 n - 1) \frac{π}{2}$ $x=+-(2n-1)pi/2$ , n =1, 2, 3, 4, .

Explanation:

$| y | = | x cos x | \leq | x |$ $|y|=|x cos x|<=|x|$

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.
$cos (\pm (2 n - 1) \frac{π}{2}) = 0$ $cos(+-(2n-1)pi/2) = 0$ , for n = 1, 2, 3, ...
So, the curve meets x-axis at (0, 0), (+-(2n-1)pi/2, 0)#, n= 1, 2, 3, ...

Limits $x \to \pm \infty$ $xto+-oo$ of x cos x are indeterminate.

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

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