(Solved): 7. Explain why the following limit notation is incorrect. \[ \begin{aligned} \lim _{x \rightarrow 1 ...

7. Explain why the following limit notation is incorrect. \[ \begin{aligned} \lim _{x \rightarrow 1} \frac{x^{2}+2 x-3}{x-1} &=\frac{(x-1)(x+3)}{x-1} \\ &=(x+3) \\ &=1+3 \\ &=4 \end{aligned} \] 8. Explain why the following limit notation is incorrect. \[ \begin{aligned} \lim _{x \rightarrow 2} \frac{x^{2}-x-2}{x-2} &=\lim _{x \rightarrow 2} \frac{(x-2)(x+1)}{x-2} \\ &=\lim _{x \rightarrow 2}(x+1) \\ &=\lim _{x \rightarrow 2}(2+1) \\ &=\lim _{x \rightarrow 2} 3=3 \end{aligned} \]