Find a curve that intersects the horizontal asymptote $y=2$ at a infinite number of points.
This is from CALC 1 limits by the way.
What I know already:
- I know that to have a horizontal asymptote you must have the numerator and the denominator be of the same degree. So to have a horizontal asymptote I would need something like $2x/x$.
- I also know that to intersect a line at infinite number of points, I would need something like a $\cos$ or a $\sin$ function. However, I can't seem to get a $\cos$ or $\sin$ function that has a horizontal asymptote at $y=2$.
$$y = 2 + {\sin (x) \over x}$$