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$1$. Let it be known that$\newline$$$\begin{array}{l} \lim _{x \rightarrow 1} f(x)=2, \lim _{x \rightarrow 10} f(x)=1, f(1)=5 ; \\ \lim _{x \rightarrow 1} g(x)=1, \lim _{x \rightarrow 10} g(x)=\frac{1}{10}, g(1)=1 . \end{array}$$$\newline$Find the limits of the functions if possible. If the boundary cannot be determined, explain why.$\newline$$1$) $\lim _{x \rightarrow 1} \frac{2 f(x)+g(x)}{f^{2}(x)}$;$\newline$$2$) $\lim _{x \rightarrow 1} g\left(\frac{f(x)}{2}\right)$;$\newline$$3$) $\lim _{x \rightarrow 1} f(2 g(x))$;$\newline$$4$) $\lim _{x \rightarrow 10} \lg (g(x))$;$\newline$$5$) $\lim _{x \rightarrow 10} 5^{f(x)}$.$\newline$$2$. Find $\lim _{x 3} f(x)$ if $6 x-9 \leq f(x) \leq x^{2}$. Explain the answer.