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lim ( n to infty) ((1)^(4) + 2^(4) + 3^...

`lim _( n to infty) ((1)^(4) + 2^(4) + 3^(4 + . . . . + n^(4)))/(n^(5)) - lim _( n to infty) ((1) ^(3) + 2 ^( 3) + 3^(3) + . . . + n ^(3))/( n^(5))` बराबर है -

A

`1//5`

B

`1//30`

C

शून्य

D

`1//4`

लिखित उत्तर

Verified by Experts

The correct Answer is:
A
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ALLEN HINDI-DEFINITE INTEGRATION-Exercise - 05 A
  1. int(0)^(1)x(1-x)^(n)dx का मान है -

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  2. lim(xto 0)((int(0)^(x^(2))sec^(2)t dt)/(x sin x)) का मान है

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  3. lim ( n to infty) ((1)^(4) + 2^(4) + 3^(4 + . . . . + n^(4)))/(n^(5))...

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  4. यदि f(y)=e^(y),g(y)=y,y gt0 तथा f(t)=int(0)^(t)f(t-y)*g(y)dy, तब

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  5. माना f(x) एक फलन इस प्रकार है कि f'(x)=f(x) तथा f(0)=1 तथा g(x) एक फ...

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  6. lim(nto oo)sum(r=1)^(n)1/n e^(r//n) का मान है

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  7. int (- 2) ^(3) | 1 - x ^(2) | dx का मान है -

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  8. I = int (0) ^( pi // 2) (( sin x + cos x )^(2))/( sqrt(1 + sin 2 x ))d...

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  9. यदि int (0) ^(pi) x f (sin x) dx = A int (0) ^( pi // 2) f ( sin x) d...

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  10. यदि f(x)=(e^x)/(1+e^x),I(1)= int(f(-a))^(f(a)) x g{x(1-x)}dx और I(2) =...

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  11. मान ज्ञात कीजिए : Lim(ntooo) [(1)/(n^(2))sec ^(2)"" (1)/(n^(2))+(2)/...

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  12. यदि I(1) = int(0)^(1)2^(x^2)dx, I(2) = int(0)^(1)2^(x^3)dx, I(3) = in...

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  13. माना F:R rarrR एक अवकलनीय फलन है तथा f(2)=6, f'(2)=((1)/(48)), तब lim(...

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  14. int (-pi)^(pi) (cos^(2)x)/(1+a^(x)) dx, a gt 0

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  15. समाकल्य int ( 3) ^( 6) ( sqrt( x))/( sqrt(9 - x) + sqrt(x)) dx का म...

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  16. int(-3pi//2)^(-pi//2) [(x+pi)^(3)+cos^(2)(x+3pi)]dx का मान है

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  17. समाकलन int (0) ^(pi) x f ( sin x ) dx का मान होगा -

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  18. int(1)^(a) [x] f'(x) dx, agt 1 का मान, जहाँ [x] महत्तम. पूर्णांक फलन ...

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  19. माना F(x) = f(x) + f(1/x), जहां f(x) = int(0)^(x)(logt)/(1+t) dt त...

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  20. समीकरण int(sqrt2)^(x)(dt)/(tsqrt(t^(2)-1))=(pi)/(2) के लिए x का मान है...

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