जाँच कीजिये कि फलन `f(x)=x^(2), x=0` पर संतत है

Explanation

` f ( 0 ) = (0)^(2)=0 " "` …(1)
` LHL = underset ( x to 0 to 0 ) lim f ( 0 - h ) `
` = underset ( h to 0 ) lim f ( -h) `
` underset ( h to 0 ) lim (-h)^(2)`
` = underset ( h to 0 ) lim h^(2) = 0 " "` …(2)
` RHL = underset ( x to 0 + 0 ) lim f ( x ) `
` = underset ( h to 0 ) lim f ( 0+h) `
` = underset ( h to 0 ) lim f ( h ) `
` = underset ( h to 0 ) lim h^(2) = 0 " "`...(3)
` :' f ( 0) = LHL = RHL `
` :. f ( x ) , x = 0 ` संतत है ।