a) From the left, the limit is 1, since
[tex]\displaystyle\lim_{x\to1^-}f(x)=\lim_{x\to1}x=1[/tex]
b) From the right, it's 2, since
[tex]\displaystyle\lim_{x\to1^+}f(x)=\lim_{x\to1}2=2[/tex]
c) Also 2, same reasoning as in (b).
d) 1, since
[tex]\displaystyle\lim_{x\to4^+}f(x)=\lim_{x\to4}(5-x)=1[/tex]
e) No, neither two-sided limits exist because the respective one-sided limits do not agree.
