For the two functions $$f(x) = \begin{cases} -1 & (|x| \geq 1) \\ 1 & (|x| < 1) \end{cases}, \quad g(x) = \begin{cases} 1 & (|x| \geq 1) \\ -x & (|x| < 1) \end{cases}$$ which of the following statements are correct? Choose all that apply from $\langle$Remarks$\rangle$. [4 points] Remarks ᄀ. $\lim_{x \rightarrow 1} f(x)g(x) = -1$ ㄴ. The function $g(x+1)$ is continuous at $x = 0$. ㄷ. The function $f(x)g(x+1)$ is continuous at $x = -1$. (1) ᄀ (2) ㄴ (3) ᄀ, ㄴ (4) ᄀ, ㄷ (5) ᄀ, ㄴ, ㄷ
For the two functions
$$f(x) = \begin{cases} -1 & (|x| \geq 1) \\ 1 & (|x| < 1) \end{cases}, \quad g(x) = \begin{cases} 1 & (|x| \geq 1) \\ -x & (|x| < 1) \end{cases}$$
which of the following statements are correct? Choose all that apply from $\langle$Remarks$\rangle$. [4 points]
\textbf{Remarks}\\
ᄀ. $\lim_{x \rightarrow 1} f(x)g(x) = -1$\\
ㄴ. The function $g(x+1)$ is continuous at $x = 0$.\\
ㄷ. The function $f(x)g(x+1)$ is continuous at $x = -1$.\\
(1) ᄀ\\
(2) ㄴ\\
(3) ᄀ, ㄴ\\
(4) ᄀ, ㄷ\\
(5) ᄀ, ㄴ, ㄷ