Question

निम्न प्रकार परिभाषति फलन ` f ( x ) ` का असांतत्यता के सभी बिंदुओं को ज्ञात कीजिये |
` f ( x ) = {{:( ( x) /(|x|)",",, "यदि " x lt 0 ) , ( - 1",",, "यदि " x gt 0 ):} `

Answer 1

हम जानते है , कि `|x| = - x ` जब ` x lt 0 `
` = x ` जब ` x gt 0 `
इसलिए ` f ( x ) = {{:( ( - x) /(x) = - 1, ",", "यदि " x lt 0 ) , ( ( x ) /(x) = 1,",","यदि " x gt 0 ) , ( 0,",", "यदि " x = 0 ):} `
`rArr f ( x) ` की सांतत्यता x = 0 पर ज्ञात करेंगे |
अब ` f ( 0 ) = 0 `
` f ( 0 - 0 ) = ` बायीं सीमा
` lim _ ( x to 0 ^(-)) f(x) = lim _ ( x to 0 ^-) ( - 1 ) = - 1 `
spasht है , कि ` f ( 0 ) ne f ( 0 - 0 ) `
` rArr ` फलन ` f ( x ) ` , बिंदु ` x = 0 ` पर सतत नहीं है |
` rArr ` फलन ` f (x) ` का असांतत्यता बिंदु x =0 है |