फलन f(x) निम्न प्रकार से परिभाषित है :
` f(x) = { ( x,"जब "0lexlt1/2 ),(0,"जब "x=1/2),(1-x,"जब "1/2ltxle1):}`
` lim_ ( x to 1//2) f(x) ` का मान ज्ञात कीजिये ।

Explanation

`R.H.L. = f( 1/2 +0) = lim _( x to 1//2+0) f(x)`
` = lim _( h to 0 ) f(1/2 +h)`
` = lim_ ( h to 0 ) [ 1-1/2-h]`
` = lim _( h to 0) [ 1/2 - h ] = 1/2`
` L. H. L = f(1/2 - 0 ) = lim _( x to 1//2 -0) f(x)`
` = lim _( h to 0) f(1/2-h)`
` = lim_( h to 0)(1/2-h)=1/2`
` R.H.L = L.H.L.`
अतः ` lim _( x to 1//2) f(x) = 1/2`