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Answer :

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.