फलन की सततता की जाँच कीजिये -
बिंदु x = 0
` f ( x ) = {{:((|sinx|)/( x )",",, x ne 0 ), ( 1",",, x = 0 ):} `

Explanation

` f ( 0 ) = 1 `
अब, ` f ( 0 + 0 ) = lim _ ( h to 0 ) f ( 0 + h ) = lim _ ( h to 0)( | sin ( 0 + h) |)/( ( 0 + h ) ) `
` = lim _ ( hto0) ( | sinh |)/(h) = lim _ ( hto 0 ) ( sin h ) /( h ) = 1 `
और ` f ( 0 - 0 ) = lim _ ( hto 0 ) f ( 0 - h ) `
` = lim _ ( hto 0 ) ( | sin ( 0 - h ) |)/( ( 0 - h )) = lim _ ( h to 0 ) (| sin ( - h )|)/( - h ) =lim _ ( h to 0 ) ( | - sin h |)/( - h ) `
` = lim _ ( h to 0 ) ( sin h ) /( -h) = - 1 `
स्पष्टतः ` f ( 0 + 0 ) ne f ( 0 - 0 ) `
अतः दिया गया फलन ` f ( x ) ` बिंदु ` x = 0 ` पर सतत नहीं है |