(a) $\displaystyle \lim_{(x,y,z) \to (4,1,2)} \frac{x^2+3z}{9y}$ is the limit of a function $f : \mathbb{R}^m \to \mathbb{R}^n$ with $m =$ and $n =$ .

(b) $\displaystyle \lim_{t \to 5} 3\cos(t) \boldsymbol{\vec{i}} + 2\sin(t) \boldsymbol{\vec{j}} + 4t \boldsymbol{\vec{k}}$ is the limit of a function $f : \mathbb{R}^m \to \mathbb{R}^n$ with $m =$ and $n =$ .

(c) $\displaystyle \lim_{(x,y) \to (\pi,2e)} \frac{\sin(xy)}{xy}$ is the limit of a function $f : \mathbb{R}^m \to \mathbb{R}^n$ with $m =$ and $n =$ .

(d) $\displaystyle \lim_{(u,v,w) \to (2\pi,7,3)} \langle e^{u^2-v^2}, 4w-6 \rangle$ is the limit of a function $f : \mathbb{R}^m \to \mathbb{R}^n$ with $m =$ and $n =$ .