Chapter 10 - Section 10.3 - Limits and Continuity: Algebraic Viewpoint - Exercises - Page 718: 20

determinate, $0$

When x$\rightarrow-\infty$, $ x^{2}\rightarrow+\infty$, $2x^{2}\rightarrow+\infty $, determinate form: $ k(\pm\infty)=\pm\infty,$ $ 3+2x^{2}\rightarrow+\infty$, determinate form: $ k\pm\infty=\pm\infty$, so the whole fraction is of the determinate form $\displaystyle \pm\frac{k}{\infty}=0$, so, the limit equals 0.