Given:
The given function f(x) approaches 0.5 when x approaches 1 from the left.
The given function f(x) approaches 1.5 when x approaches 1 from the right.
Required:
We need to find the limit of f(x).
Explanation:
There is a jump discontinuity.
The given function f(x) approaches 0.5 when x approaches 1 from the left.
[tex]Left-\text{hand limit =0.5}[/tex]The given function f(x) approaches 1.5 when x approaches 1 from the right.
[tex]Right-\text{hand limit =1.5}[/tex][tex]\text{We know that }0.5\ne1.5.[/tex][tex]Left-\text{hand limit }\ne Right-\text{hand limit.}[/tex]The limit does not exist at x =1 in the given graph.
Final answer:
The limit does not exist at x =1 in the given graph because the left hand-limit is not equal to the right-hand limit.