फलन`f(x)` जिसके लिए
` f(x) {: {(x^(2),x !=1),(2,x=1):}`
दिखाइए कि ` lim _( x to 1) f( x) = 1 `

Explanation

` lim_ ( x to 1+0) f(x) = lim _ ( x to 1 + 0) f( 1 + h) = lim _ ( h to 0) ( 1 + h)^(2) = 1 `
और `lim_ ( x to 1 - 0 ) f ( x) = lim _ ( x to 1 - 0 ) f ( 1- h) = lim _ ( h - 0) ( 1- h)^(2) = 1 `
` :. lim _ ( x to 1 + 0 ) f( x) = lim _ ( x to 1 -0) f ( x) = 1 `
अतः ` lim _( x to 1) f(x) = 1 `