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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, .

#|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.

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Answer 2

Delilah Aguilar

To graph the function ( y = x \cos(x) ), you can follow these steps:

Determine the key features of the graph, such as the intercepts, extrema, and behavior as ( x ) approaches positive and negative infinity.
Plot several points on the graph by choosing various values of ( x ) and calculating the corresponding values of ( y ) using the function.
Connect the points smoothly to form the graph of the function.

You may also want to consider using technology such as graphing calculators or graphing software to create an accurate graph of the function.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.