यदि `f(x)={{:("3ax+b,",ifxgt1),("11,",if x=1),(5ax-2b,ifxlt1):},x=1`

Explanation

`f (1) = 11 " "`…(i)
बायीं सीमा ` underset (x to 0- 0 ) lim f ( x) = underset (hto 0 ) lim f (1-h) `
` = underset ( h to 0 ) lim { 5 a ( 1 - h ) - 2b}`
` 5a - 2a " " …(ii) `
दायी सीमा ` = underset ( x to 1 + 0 ) lim f ( x)= underset (h to 0 ) f ( 1+h)`
` = underset (h to 0 ) lim {3a (1+h)+b}`
` 3a + b " "` ...(iii)
यदि `f(x),x=1` पर संतत है तो
बायीं सीमा = दायी सीमा = f(1)
या `5a - 2b = 3a + b = 11`
ya `5a - 2b = 11" "...(iv) `
`3a+b=11" " `...(v)
समीकरण (iv) व (v) को हल करने पर,
`a=3,b=2`