InterviewSolution
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InterviewSolution
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यदि फलन `f(x)={{:((x^(2)-4)/(x-2),xne2),("k,",x=2):}x=2` पर संतत है तो k का मान ज्ञात कीजिये । |
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Answer» `f(2) = k ` दायी सीमा ` = underset ( x to 2 + 0) lim f ( x ) ` ` = underset ( h to 0 ) lim f(2+h) ` ` = underset ( h to 0 ) lim ((2+h)^(2)-4)/(2+h-2) ` ` = underset ( h to 0 ) lim (4 + h ^(2) + 4h - 4 )/h` `underset ( h to 0 ) lim ( h + 4) = 4 ` बायीं सीमा ` = underset ( x to 2 - 0 ) lim f ( x) ` ` = underset ( h to 0 ) lim f ( 2 - h ) ` ` = underset (h to 0 ) lim (( 2-h)^(2) - 4 )/(2-h -2)` `= underset ( h to 0 ) lim ( 4+h^(2) - 4h - 4 )/(-h)` ` = underset ( h to 0 ) lim ( 4 - h ) = 4 ` यदि फलन `f(x),x = 2 ` पर संतत है तो दायी सीमा = बायीं सीमा = k ` " या " 4=4 = k " या " k=4 ` |
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