I am trying to compute the following limit and am trying to determine a way to compute
$$f(\mu _1,\mu _2,\mu _3,\mu_4)=\frac{\lambda \mu _2 \mu _3}{\left(\mu _2-\mu _1\right) \left(\lambda ^3+\mu _3 \left(2 \lambda ^2+\mu _2 \left(2 \lambda +\mu _1\right)\right)\right)}.$$
The equation "blows up" when $(\mu _1,\mu _2,\mu _3,\mu_4)\rightarrow (1 ,1,1,1)$.
$$\lim_{(\mu _1,\mu _2,\mu _3,\mu_4)\rightarrow (1 ,1,1,1)} f(\mu _1,\mu _2,\mu _3,\mu_4)$$
I tried using L'Hopital's rule, but the problem is that it does not apply to multivariable calculus.
Any direction would be greatly appreciated...
$$f(\mu _1,\mu _2,\mu _3,\mu_4)=\frac{\lambda \mu _2 \mu _3}{\left(\mu _2-\mu _1\right) \left(\lambda ^3+\mu _3 \left(2 \lambda ^2+\mu _2 \left(2 \lambda +\mu _1\right)\right)\right)}$$ When the $\mu_i \to 1$, this reduces to $$\frac {\lambda}{\left(\mu _2-\mu _1\right)(\lambda +1) \left(\lambda ^2+\lambda +1\right) }$$ and then $\cdots$