फलन ` f ( x ) ` की ` x = 1, ` पर सांतत्यता का परीक्षण कीजिये, यदि
`f(x ) = {{:( 1 + x ^(2),”,”,”यदि ” 0 le x le 1 ), ( 1 – x,”,”, “यदि ” x gt 1):} `
`f(x ) = {{:( 1 + x ^(2),”,”,”यदि ” 0 le x le 1 ), ( 1 – x,”,”, “यदि ” x gt 1):} `
Correct Answer – असतत
` RHL = f ( 1 + 0 ) = lim_ ( hto 0 ) f ( 1 + h ) = lim _ ( hto 0 ) [ 1 – ( 1 + h ) ] `
` = 0 `
` LHL = f ( 1 – 0 ) = lim _ ( h to 0 ) f( 1 -h) = lim _ ( h to 0 ) [ 1 + ( 1- h ) ^(2) ] `
`lim _ ( h to 0 ) ( 2 + h ^2 – 2 h ) = 2 `
स्पष्टता: RHL `ne ` LHL