Question

The graph of a function f is shown above. If lim f (x) exists, and f is not continuous at2= b, then b=

Answer 1

Recall that

`\lim_(x\to b)f(x)`

exists if and only if:

`\lim_(x\to b^-)f(x)=\lim_(x\to b+)f(x).`

Now, from the given graph we get that:

`\begin{gathered} \lim_(x\to0^+)f(x)=2, \\ \lim_(x\to0^-)f(x)=2, \end{gathered}`

Then:

`\lim_(x\to0^-)f(x)=\lim_(x\to0^+)f(x).`

Therefore:

`\lim_(x\to0)f(x)`

exists.

Now, from the given graph we get that:

`f(0)<2.`

Therefore f(x) is not continuous at x=0.

Answer: b=0.