बिंदु ` x = 0 ` पर ` f ( x ) ` की सततता की जाँच कीजिये -
` f ( x ) = {{:( ( x - |x|) /( x )",",, x ne 0 ) ,(2",",, x = 0):} `

Explanation

x =0 पर ` f ( x ) = 2 rArr f ( 0 ) = 2 `
अब `|x| = x ` यदि ` x gt 0 ` और ` - x ` यदि ` x lt 0 `
` therefore f ( x ) = ( x - x ) /(x) = 0 ` जब ` x gt0 `
` = ( x - ( - x ) ) /( x ) = 2 ` जब ` x lt 0 `
अतः ` f ( 0 + 0 ) = lim _ ( hto 0 ) f ( 0 +h ) = lim _ ( hto 0 ) 0 = 0 `
और ` f ( 0 -0) = lim _ ( h to 0) f( 0 -h) = lim _ ( hto 0 ) 2 = 2 `
` rArr f ( 0 + 0 ) ne f ( 0 - 0 ) `
अतः ` x = 0 ` पर ` f (x ) ` सतत नहीं है |