Question

Determine if the lim f(x) exists using the graph below.. If it does, find its value. If it does not,x 1explain why

Answer 1

The limit of a function f at a point a exists if:

`\lim_(x\to a^-)f(x)=\lim_(x\to a^+)f(x)`
`\begin{gathered} \text{ From the given image, the value of the left limit of f at x=1 } \\ \lim_(x\to a^-)f(x)\lt1 \end{gathered}`

Also,

`\begin{gathered} \text{ From the given image, the value of the right limit of f at x=1 } \\ \lim_(x\to a^+)f(x)\gt1 \end{gathered}`

Therefore,

`\lim_(x\to1^-)f(x)\lim_(x\to1^+)f(x)`

Hence, the limit does not exist