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