दिखाए कि फलन `f(x)={{:(x^(3)+3,if,xne0),(1,if,x=0):}x=0` पर संतत नहीं है

Explanation

`f(0)=1 ` ...(1)
`LHL = underset(x rarr 0-0)lim f(x)`
`= underset(h rarr 0) lim f(0-h)`
`=underset(h rarr 0 ) lim f(-h)`
`=underset(hrarr0)lim {(-h)^(3)+3}`
`=underset(hrarr0)lim (-h^(3)+3)`
`=3` ...(2)
`RHL=underset(x rarr 0 + 0 ) lim f(x)`
`= underset(h rarr 0 ) lim f (0+h)`
`= underset(h rarr 0 ) lim f (h)`
`= underset(h rarr 0 ) lim (h^(3) + 3) =3 ` ...(3)
`:' LHL = RHL != f (0)`
`:. f(x), x(0)` पर संतत नहीं है । ( इति सिध्दम )