12.4 Compute the limits, then verify or refute the statement

$$
\lim _{x \rightarrow 3} \frac{x^{2}+x-12}{3 x-9}=5+\lim _{x \rightarrow 2} \frac{x^{4}-16}{8-x^{3}}
$$

Find the derivatives of the functions (12.5-12.7):


12.4 We find

$$
\lim _{x \rightarrow 3} \frac{x^{2}+x-12}{3 x-9}=2 \frac{1}{3}(1) ; 5+\lim _{x \rightarrow 2} \frac{x^{4}-16}{8-x^{3}}=5-2 \frac{2}{3}=2 \frac{1}{3}
$$

From (1) and (2) it follows that the given equality is correct.