दिखाइए कि फलन `f(x)=2x+3,x=1` पर संतत है

Explanation

` f ( 1 ) = 2 (1) + 3 = 5 `
` LHL = underset (x to 1-0 ) lim f ( x )" "` …(1)
` = underset (h to 0 ) lim f ( 1 - h ) `
` = underset ( h to 0 ) { 2 ( 1 - h ) `
` = underset ( h to 0 ) lim { 2 ( 1 - h ) + 3 }`
` 2 + 3 + = 5 `
` RHL = underset ( x to 1 + 0 ) lim f(x) `
` = underset ( h to 0 ) lim f ( 1 + h ) `
` = underset ( h to 0 ) lim {2 ( 1 + h ) 3 }`
`=2+3`
`=5" " `...(3)
` :' f ( 1) = LHL = RHL `
` :. f (x) , x = 1 `पर संतत है ।