Question
Medium
Solving time: 3 mins
Show that the function defined by is discontinuous at all integral point. Here denotes the greatest integer less than or equal to x.
Text solutionVerified
The given function is g(x)=x-[x]
It is evident that g is defined at all integral points.
Let n be an integer.
Then,
The left hand limit of f at x=n is,
The right hand limit of fat x=n
It is observed that the left and right hand limits of fat x=n do not coincide.
Therefore, f is not continuous at x=n
Hence, g is discontinuous at all integral points.
It is evident that g is defined at all integral points.
Let n be an integer.
Then,
The left hand limit of f at x=n is,
The right hand limit of fat x=n
It is observed that the left and right hand limits of fat x=n do not coincide.
Therefore, f is not continuous at x=n
Hence, g is discontinuous at all integral points.
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Question Text | Show that the function defined by is discontinuous at all integral point. Here denotes the greatest integer less than or equal to x. |
Updated On | Jan 7, 2024 |
Topic | Continuity and Differentiability |
Subject | Mathematics |
Class | Class 12 |
Answer Type | Text solution:1 Video solution: 8 |
Upvotes | 821 |
Avg. Video Duration | 7 min |