Answer
$$\lim _{x \rightarrow 3} \frac{3 x^{2}+2}{2 x^{2}+3 }=\frac{29}{21}$$
Work Step by Step
Given $$\lim _{x \rightarrow 3} \frac{3 x^{2}+2}{2 x^{2}+3}$$
using the method of replacement
\begin{align*}
\lim _{x \rightarrow 3} \frac{3 x^{2}+2}{2 x^{2}+3}&=\lim _{x \rightarrow 3} \frac{3 (3)^{2}+2}{2 (3)^{2}+3}\\
&=\lim _{x \rightarrow 3}\frac{29}{21}\\
&=\frac{29}{21}
\end{align*}
