There are two horizontal asymptotes in the graph of a signum function. So, there should practically be 2 values of 'y' for x=infinity. Please explain this.

Asked by Varunasav | 27th Sep, 2014, 07:32: PM

Expert Answer:

A space l i n e space i s space a n space a s y m p t o t e space i f space i t space s a t i s f i e s space a t space l e a s t space o n e space o f space t h e space f o l l o w i n g space s t a t e m e n t s : limit as x rightwards arrow a of f left parenthesis x right parenthesis equals plus-or-minus infinity comma limit as x rightwards arrow infinity of f left parenthesis x right parenthesis equals c comma limit as x rightwards arrow infinity of f left parenthesis x right parenthesis minus left parenthesis m x plus n right parenthesis equals 0 F o r space a space s i g n u m space f u n c t i o n comma space F o r space x rightwards arrow infinity comma limit as x rightwards arrow infinity of space f left parenthesis x right parenthesis equals 1 y equals 1 space i s space t h e space a s y m p t o t e space i n space t h i s space c a s e F o r space x equals 0 comma space y equals 0 F o r space x rightwards arrow minus infinity comma limit as x rightwards arrow minus infinity of space f left parenthesis x right parenthesis equals minus 1 y equals minus 1 space i s space t h e space a s y m p t o t e space i n space t h i s space c a s e.

Answered by Prasenjit Paul | 29th Sep, 2014, 12:27: PM

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