Lorena Lester

2022-07-14

Finding the asymptotes
Find the asymptotes for $F\left(x\right)=ln\left({x}^{2}=-3\right)$. I realise there is no vertical asymptote since ${X}^{2}=-3$. I want to know if the horizontal asymptote exist

grocbyntza

Expert

No, since $\underset{x\to ±\mathrm{\infty }}{lim}F\left(x\right)=\mathrm{\infty }$.
Inded, if $M\in \mathbb{R}$ and $|x|>{e}^{M/2}$
then $F\left(x\right)=\mathrm{ln}\left({x}^{2}+3\right)>\mathrm{ln}\left({x}^{2}\right)>\mathrm{ln}{e}^{M}=M$

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