Question

यदि फलन
` f ( x ) = {{:( 3ax + b",",, "यदि" x gt 1 ), ( 11,",", "यदि" x = 1 ), ( 5ax - 2 b",",, "यदि" x lt 1 ):} `
बिंदु x = 1 पर सतत है, तो a व बी के मान ज्ञात कीजिये |

Answer 1

प्रश्नानुसार फलन ` f ( x ) , x = 1 ` पर सतत है | ` therefore f (1 + 0) = f ( 1 - 0 ) = f ( 1 ) `
अब ` f ( 1 - 0 ) = lim _ ( x to 1 ^-) f ( x )`
` = lim _ ( x to 1^-) ( 5ax- 2b ) = 5 a - 2b ` ... (1)
`f (1 +0 ) = lim _ ( xto 1^+) f (x) = lim _ ( x to 1^+) ( 3ax + b ) = 3a + b `...(2)
तथा ` f(1) = 11 `
समीकरण ` (1), (2) ` व ` (3)`को हल करने पर
` a = 3, b = 2 `