दिखाइये कि ` f(x)= {:{(x^(2) , x!= 1),(2, x=1):} " बिंदु " x=1` पर असंतत है ।

Explanation

दिया हुआ है , f(1) = 2
`lim _(h to 0 ) ( 1 + h ) ^(2) = 1 `
और ` lim _ ( x to 1 - 0 ) f( x ) = lim _ ( h to 0 ) f ( 1-h ) `
` = lim _(h to 0 ) (1 - h )^(2) = 1 `
` :. lim _(x to 1 ) f (x) = 1 != f(1)`
अतः फलन `x=0` पर असंतत है ।