\(A. \rightarrow \displaystyle\lim_{x\to-\infty}\frac{x^2+x-12}{x\,-\,3}=\lim_{x\to-\infty}\frac{x^2}{x}=\lim_{x\to-\infty}x=-\infty\)
\(B. \rightarrow \displaystyle\lim_{x\to+\infty}\frac{x^2+x-12}{x\,-\,3}=\lim_{x\to+\infty}\frac{x^2}{x}=\lim_{x\to+\infty}x=+\infty\)
\(C. \rightarrow \displaystyle\lim_{x\to+3}\frac{x^2+x-12}{x\,-\,3}=\lim_{x\to+3}\frac{(x-3)(x+4)}{x-3}=\lim_{x\to+3}(x+4)=7\)
\(D. \rightarrow \displaystyle\lim_{x\to+4}\frac{x^2+x-12}{x\,-\,3}=\frac81=8\)
\(E. \rightarrow \displaystyle\lim_{x\to-4}\frac{x^2+x-12}{x\,-\,3}=\lim_{x\to-4}\frac{(x-3)(x+4)}{x\,-\,3}=\lim_{x\to-4}(x+4)=0\)