सिद्ध कीजिये कि फलन `f(x)={{:(("sin x")/x,if,xlt0),(x+1,if,xge0):}` एक संतत फलन है ।

Explanation

`f(0) = 0+1=1" " `…(1)
`LHL = 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 (sin (-h))/-h `
` = underset (h to 0 )lim (-sin h )/-h`
` = underset (h to 0 )lim (sin h )/h`
` = underset (h to 0 )lim (sin h )/h`
`=1 " " ...(2)`
`RHL = underset (x to 0 +0)lim f(x)`
`= underset (h to 0 ) lim f(h)`
` = underset ( h to 0 ) lim ( sin h )/h `
`=1 " " ...(3)`
` :' LHL = RHL = F(0)`
` :. f(x), x= 0 ` पर एक संतत फलन है ।