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One-sided limits

In many cases it is more easy to investigate the behaviour of a function when x approaches a given value c from the left or from the right. More precisely:

• If x → c and x>a, we write x → c⁺ and get right-hand limit.
• If x → c and x<a, we write x → c^- and get left-hand limit.

There is a theorem that highlights the importance of these concepts: exists if and only if  and both exist and are equal.

Consider the following picture.

From the graph wededuce:

• 
• 
• 
• , while f(2) = 1.5
• 

 

copyright 2000 et seq. maddalena falanga & luciano battaia

first published on march 26 2002 - last updated on september 01 2003