Does xcos(x) have oblique asymptotes? Looking at the graph of xcos(x) or xsin(x) etc., it looks like the magnitude of the waves are following a line. Are they oblique asymptotes or something else? I am familiar with finding the oblique asymptotes of a rational function like P(x)/Q(x) by dividing Q(x) into P(x); however, it doesn't seem like I can do that with xcos(x) et al. what is going on here? and how would you find the equation of the function that is 'controlling' the original function's behavior?

spatularificw2

spatularificw2

Answered question

2022-09-01

Does xcos(x) have oblique asymptotes?
Looking at the graph of xcos(x) or xsin(x) etc., it looks like the magnitude of the waves are following a line. Are they oblique asymptotes or something else?
I am familiar with finding the oblique asymptotes of a rational function like P ( x ) Q ( x ) by dividing Q(x) into P(x); however, it doesn't seem like I can do that with xcos(x) et al. what is going on here? and how would you find the equation of the function that is 'controlling' the original function's behavior?

Answer & Explanation

recepiamsb

recepiamsb

Beginner2022-09-02Added 9 answers

For a line to count as an asymptote, the distance between that line and the graph of the function has to tend to zero.
This doesn't hold in your examples, so the lines are not asymptotes.

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