QuestionSketch the graph of the piecewise function and find the limits:
1. For $f(x) = \begin{cases} \sin x & x < 0 \\ x^2 & 0 \leq x < 2 \\ x & x \geq 2 \end{cases}$, find: i. $\lim_{x \to 0} f(x)$ ii. $\lim_{x \to 2} f(x)$
2. For $f(x) = \begin{cases} e^x & x \leq 0 \\ |x| + 1 & 0 < x < 1 \\ \ln x & x \geq 1 \end{cases}$, find: i. $\lim_{x \to 0} f(x)$ ii. $\lim_{x \to 1} f(x)$