$12.36 \lim _{x \rightarrow 1} \frac{\sqrt[3]{x}-1}{\sqrt[3]{x^{2}+2 \sqrt[3]{x}-3}}$.

Calculate the limits, and then confirm or refute the following statements ( $12.37-12.38$ ):
12.36 Factor the denominator of the fraction:

$$
\sqrt[3]{x^{2}}+2 \sqrt[3]{x}-3=(\sqrt[3]{x}-1)^{2}+4 \sqrt[3]{x}-4=(\sqrt[3]{x}-1)(\sqrt[3]{x}+3)
$$

Now, by canceling the fraction by $\sqrt[3]{x}-1 \neq 0$, we find

$$
\lim _{x \rightarrow 1} \frac{1}{\sqrt[3]{x}+3}=\frac{1}{4}
$$

Answer: 0.25 .