Question

Determine if each statement is True or False based on the graph

Answer 1

a)

`\begin{gathered} \lim _(x\to2^-)f(x)=3 \\ _{\text{ }}False \end{gathered}`

b)

`\begin{gathered} \lim _(x\to2^+)f(x)=0 \\ _{\text{ }}False \end{gathered}`

c)

`\begin{gathered} \lim _(x\to2^-)f(x)=\lim _(x\to2^+)f(x) \\ _{\text{ }}False \end{gathered}`

d)

`\begin{gathered} \lim _(x\to2)f(x)_{\text{ }}exists \\ _{\text{ }}False \end{gathered}`

e)

`\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}`

f)

`\begin{gathered} \lim _(x\to4)f(x)=f(4) \\ _{\text{ }}False \\ f(4)=-1 \end{gathered}`

g) f is continuous at x = 4:

`\begin{gathered} _{\text{ }}false \\ \lim _(x\to4)f(x)\\e f(4) \end{gathered}`

h) f is continuous at x = 0

`_{\text{ }}True`

i)

`\begin{gathered} \lim _(x\to3)f(x)=\lim _(x\to5)f(x)=3 \\ True_{\text{ }} \end{gathered}`

j) f is continuous at x = 2?

False