One-Sided Limits

    When  we can make the number as close to as we please by choosing sufficiently close to on a small interval immediately to the right of we write



Similarly, when we can make the number as close to as we please by choosing sufficiently close to on a small interval immediately to the left of we write

Example (Limits Using Tables) Find the limit of as approaches from the left using a table of functional values for   and

    Solution. We compute,
    
  
  
Thus as approaches from the left we estimate approaches Therefore,  we estimate that

        

Example (Limits Using Graphs) Find the limit of as approaches from the left using a graph of the function around c for and

    Solution. We find,


Thus as x approaches from the left we estimate approaches Therefore, we estimate

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Cite this as:
One Sided Limits
Published by Library of Math -- Online math organized by subject into topics.
Written by Smith, David A.
http://www.libraryofmath.com/one-sided-limits.html