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यदि f(x) = {:{(x-4,"जबकि "x ge 5),(5x-...

यदि ` f(x) = {:{(x-4,"जबकि "x ge 5),(5x-24,"जबकि "x lt 5):}`
तो दर्शाइए कि` f(x),x=5` पर एक संतत फलन है ।

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MANOHAR RAY-सततता तथा अवकलनीयता -प्रश्नावली 5(A)
  1. x=3 पर फलन f(x) =2x^(2) - 1 के सांतत्य कि जाँच कीजिए ।

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  2. निम्नलिखित फलनों के सांतत्य कि जाँच कीजिए : (a) f(x) = x-5 ...

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  3. यदि f(x) = {:{(x-4,"जबकि "x ge 5),(5x-24,"जबकि "x lt 5):} तो दर्...

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  4. सिद्ध कीजिए कि फलन f(x) = x^(n) , x = n पर संतत है , जहाँ n एक प...

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  5. क्या f(x) = {:{(x ,"यदि " x le 1 ),(5,"यदि"x gt 1 ):} द्वारा परिभ...

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  6. f(x) = {:{((sin^(2)ax)/(x^(2)),x !=0),(1,x=0" पर "):}

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  7. f(x) = {:{ ("sin"1/x,x !=0), (1,x=0" पर संतत है अथवा असंतत ।") :}

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  8. f(x) = {:{((|x-3|)/(x-3),x!= 3),(0,x=3):}.

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  9. f(x) = {:{(3,"if "0 le x le 1),(4,"if "1 lt x lt 3),(5,"if " 3 le...

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  10. f(x) = {:{(2x,"यदि "x lt 0),(0,"यदि " 0 le x le 1 ),(4x,"यदि"x gt 1...

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  11. f(x) = {:{ (-2," यदि " x le -1 ) , (2x," यदि " -1 lt x le 1 ),(2," य...

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  12. दिखाइए कि f(x) = {:{( 1/(1-e^(1//x)), x != 0),(0,x=0 ):} पर फलन असं...

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  13. f(x) = {:{((x^(2)-4)/(x-2),x !=2 ),(4,x=2 " पर संतत है अथवा असंतत ।")...

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  14. f(x) = {:{(2x+3," यदि " x le 2 ),(2x-3," यदि "x gt2):}

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  15. f(x) = {:(2x+3," यदि " x le 2 ),(2x-3," यदि "x gt2):}

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  16. f(x)= {:{(|x|+3," "x le -3),(-2x," " -3 lt x lt 3 ),(6x+2," " x ge 3 )...

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  17. f (x) = {:{((|x|)/x," यदि " x !=0),(0," यदि " x=0):}

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  18. f(x) ={: (x+1,"यदि " x le 1), (x^(2) +1 ,"यदि " x lt1):}

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  19. f(x) = {:(x^(3)-3," यदि " x le 2 ),(x^(2)+1," यदि "x gt 2):}

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  20. f(x) {:(x^(10) -1,"यदि " x le 1),(x^(2) ,"यदि " x gt 1 ):}

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