Recently, I have been studying limits of multivariable functions.
In particular, I am interested to evaluate the expression $$\displaystyle \frac{1}{(4 \left((\alpha + 2 y\beta + x \delta)^2 + (\epsilon +2 y \eta + x \lambda)^2\right)^2 \left(\left(y \delta + a_{10} + 2 x a_{20})^2 + (y \lambda + b_{10}+ 2xb_{20})^2\right))^2\right)}$$.
in the neighborhood of $y=0$ and $x=\displaystyle \frac{(-\delta \epsilon \sqrt{-(\delta \eta - \beta\lambda)^2} \ + \alpha \lambda \sqrt{-(\delta \eta - \beta \lambda)^2} - \ \delta \eta (\alpha \delta + \epsilon \lambda) + \beta \ \lambda (\alpha \delta + \epsilon \lambda))}{((\delta \ \eta - \beta \lambda) (\delta^2 + \lambda^2))}$.
By employing the Mathematica, one retrives $\textit{ComplexInfinity}$ as a result. Based on the above,
- What does $\textit{ComplexInfinity}$ mean here? That is to say, what is the suppose direction of a such result (e.g. -$\infty$ or +$\infty$ or just $\infty$ ?
- Is there another way to evaluate that limit and obtain a more reliable result through Mathematica or Maple?
Ps: I have read other posts on the subject, however, these did not clarify my doubts.
