JamesBwoii said:Homework Statement
Draw a graph of xcos(1/x)
2. The attempt at a solution
I've differentiated the equation using the product rule.
This got me to:
cos(1/x) + sin(1/x)/x
What I don't know how to do is actually go about drawing the graph. This is also a past paper question for an exam where I won't be allowed calculators.
Thanks!
The graph of xcos(1/x) is a continuous, oscillating curve. As the value of x approaches 0, the curve becomes more and more compressed, with infinitely many oscillations.
The x intercepts occur at 0 and all points where x = 1/(2nπ) for n = 1, 2, 3, ... The y intercepts occur at 1 and -1.
No, the graph of xcos(1/x) is not symmetrical. It has a vertical asymptote at x = 0, which creates a discontinuity in the curve.
The domain of the graph is all real numbers except 0. The range is the set of all real numbers between -1 and 1, inclusive.
As x approaches 0, the graph of xcos(1/x) becomes more and more compressed, with infinitely many oscillations. The curve also becomes steeper, approaching the vertical asymptote at x = 0.