a)
[tex]\begin{gathered} \lim _{x\to2^-}f(x)=3 \\ _{\text{ }}False \end{gathered}[/tex]
b)
[tex]\begin{gathered} \lim _{x\to2^+}f(x)=0 \\ _{\text{ }}False \end{gathered}[/tex]
c)
[tex]\begin{gathered} \lim _{x\to2^-}f(x)=\lim _{x\to2^+}f(x) \\ _{\text{ }}False \end{gathered}[/tex]
d)
[tex]\begin{gathered} \lim _{x\to2}f(x)_{\text{ }}exists \\ _{\text{ }}False \end{gathered}[/tex]
e)
[tex]\begin{gathered} \lim _{x\to4}f(x)_{\text{ }}exists;_{\text{ }}True \\ _{\text{ }}since \\ \lim _{x\to4^-}f(x)=3_{\text{ }} \\ \lim _{x\to4^+}f(x)=3_{\text{ }} \end{gathered}[/tex]
f)
[tex]\begin{gathered} \lim _{x\to4}f(x)=f(4) \\ _{\text{ }}False \\ f(4)=-1 \end{gathered}[/tex]
g) f is continuous at x = 4:
[tex]\begin{gathered} _{\text{ }}false \\ \lim _{x\to4}f(x)\ne f(4) \end{gathered}[/tex]
h) f is continuous at x = 0
[tex]_{\text{ }}True[/tex]
i)
[tex]\begin{gathered} \lim _{x\to3}f(x)=\lim _{x\to5}f(x)=3 \\ True_{\text{ }} \end{gathered}[/tex]
j) f is continuous at x = 2?
False
