यदि फलन `f(x)={{:((x^(2)-4)/(x-2),xne2),("k,",x=2):}x=2` पर संतत है तो k का मान ज्ञात कीजिये ।

Explanation

`f(2) = k `
दायी सीमा ` = underset ( x to 2 + 0) lim f ( x ) `
` = underset ( h to 0 ) lim f(2+h) `
` = underset ( h to 0 ) lim ((2+h)^(2)-4)/(2+h-2) `
` = underset ( h to 0 ) lim (4 + h ^(2) + 4h - 4 )/h`
`underset ( h to 0 ) lim ( h + 4) = 4 `
बायीं सीमा ` = underset ( x to 2 - 0 ) lim f ( x) `
` = underset ( h to 0 ) lim f ( 2 - h ) `
` = underset (h to 0 ) lim (( 2-h)^(2) - 4 )/(2-h -2)`
`= underset ( h to 0 ) lim ( 4+h^(2) - 4h - 4 )/(-h)`
` = underset ( h to 0 ) lim ( 4 - h ) = 4 `
यदि फलन `f(x),x = 2 ` पर संतत है तो
दायी सीमा = बायीं सीमा = k
` " या " 4=4 = k " या " k=4 `