Math CentralQuandaries & Queries


Question from rimoshika, a student:

find a function that have 3 Asymptotic : y=x/y=sinx/x=-1

Hi Rimoshika,

I would define the function in two pieces, one for $x < -1$ and the other for $x > -1.$ I can help with the part for $x < -1.$

For $x < -1$ define a function $f(x) = g(x) \sin x$ where $g(x)$ is a function that satisfies $\lim g(x) = 1$ as $x \rightarrow -\infty$ and $\lim g(x) = \pm \infty$ as $x \rightarrow -1.$ The $f(x)$ will have $y = \sin x$ and $x =-1$ as asymptotes.


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