k के किस मान के लिए फलन

Explanation

` :' ` x= 3 पर f(x) का मान k है ,
` :. f(3 )= k`
` x=3 " पर " , L.H.L = lim _( x to 3 + 0 ) f(x) `
` = lim _( h to 0) f ( 3 + h)`
` = lim _ (h to 0) ((3+h)^(2) -9)/(3+h -3)`
` = lim _( h to 0) ( 9 + h^(2) + 6h - 9)/( 3 + h - 3) `
` = lim _( h to 0 ) ( h (h +6))/h`
`= lim_( h to 0) ( h + 6) " " [ :' h != 0]`
=6
इसी प्रकार `R.H.S = lim _(h to 3 - 0 ) f ( x) `
`=lim _(h to 0) f( 3-h) `
` = lim _(h to 0) ((3 -h)^(2) -9)/((3-h)-3) `
` lim _( h to 0) ( 9 + h^(2) - 6h - 9)/( 3- h-3) `
`= lim_(h to 0) (h ( h-6))/(-h) `
` = lim _ (h to 0) (-h + 6) , " " [ :' h !=0 ] `
= 6
लेकिन दिया है की फलन`x=0` पर संतत है ।
` :. L.H.L = R.H .L = f(3)` .
` :. 6 = 6 = k`
` :. k = 6 `