47. Find the limit of the function:
1) $f(x)=x^{3}-5 x^{2}+2 x+4$ as $x \rightarrow-3$;
2) $\varphi(t)=t \sqrt{t^{2}-20}-\lg \left(t+\sqrt{t^{2}-20}\right)$ as $t \rightarrow 6$.
Solution. The given function is elementary, it is defined at the limit point, so we find the limit of the function as its particular value at the limit point:

1) $\lim _{x \rightarrow-3} f(x)=f(-3)=(-3)^{3}-5 \cdot(-3)^{2}+2 \cdot(-3)+4=-74$;
2) $\lim \varphi(t)=\varphi(6)=6 \sqrt{6^{2}-20}-\lg \left(6+\sqrt{6^{2}-20}\right)=23$.

Find the following limits: