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underset( x to 0 )Lim (underset( 0)overs...

` underset( x to 0 )Lim (underset( 0)overset( 1)int (by +a( 1-y ) )^(x) dy ) ^(1//x) ` (जहाँ `b ne a) `

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The correct Answer is:
` e^(-1) ((b^(b))/( a^(a)) ) ^((1)/(b-a)) `
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BANSAL HINDI-INDEFENITE & DEFINITE INTEGRATION -EXERCISE -2 (SECTION -B (DEFINITE INTEGRATION ) )
  1. माना y= f(x) एक द्विघातीय फलन है जहाँ f'(2) =1 है , तो समाकलन unde...

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  2. माना की f(x)= {:{ ([ -1], if -2 le x le 0 ),( |x-1| , if 0lt xle 2 ...

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  3. फलन f(x) = {:{( underset( 0)overset( x )int (5+ 2|t-1|) dt , x gt 2 ),...

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  4. यदि y= x ^(underset( 1 )overset( x) int lnt dt ) है , तो (dy)/(dx)...

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  5. अचर 'a' (a gt 0 ) एवं 'b ' ज्ञात करों जो इस प्रकार है की underset(...

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  6. underset( x to infty ) Lim (d)/(dx) underset ( 2 sin ""(1)/(x))overse...

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  7. underset( 0 )overset( infty ) int (lnt )/(x^(2) +t^(2)) dt= ( piln 2...

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  8. underset( a to infty ) Lim (underset(0 )overset( a)int sin ^(4) x dx ...

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  9. underset( x to 0 )Lim (underset( 0)overset( 1)int (by +a( 1-y ) )^(x) ...

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  10. यदि log (beta +3) (alpha ^(2) -2) = log (beta -6) (2alpha -3) =u...

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  11. माना a ,b वास्तविक संख्याये इस प्रकार है की a+b=1 है ,तो समाकलन under...

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  12. एक धनात्मक ,सतत एवं अवकलनीय फलन f ज्ञात करों जो x के प्रत्येक मान के ल...

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  13. माना f(x),R पर परिभाषित फलन निम्न प्रकार से है f'(x) =f'(3-x) AA ...

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  14. lim(n to oo) [(1+1/(n^(2)))(1+(2^(2))/(n^(2)))+....(1+(n^(2))/(n^(2)))...

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  15. underset(nto infty ) Lim (1)/(n) [(1)/( n+1) +(2)/( n+2) +.........

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  16. मान ज्ञात कीजिए : Lim (n to infty) [ (n !)/( n^(n))]^(1//n)

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  17. माना Pn =" " ^(n) sqrt( ((3n )!)/( (2n )!) ) (n =1,2,3......) तो und...

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  18. दिया गया है की In = underset( 0)overset( 1) int (1+ x^(2)) ^(n) dx ...

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  19. माना f एवं g,x के प्रत्येक मान के लिए अवकलनीय है तथा निम्नलिखित गुण ...

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  20. यदि Un =underset( 0) overset( pi//2) int (sin ^(2) nx)/( sin ^(2...

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