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The value of lim(n rarr oo) (1 + 2^(4) +...

The value of `lim_(n rarr oo) (1 + 2^(4) + 3^(4) +…...+n^(4))/(n^(5)) - lim_(n rarr oo) (1 + 2^(3) + 3^(3) +…...+n^(3))/(n^(5))` is :

A

zero

B

(1/4)

C

(1/5)

D

(1/30)

Text Solution

Verified by Experts

The correct Answer is:
C
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HIMALAYA PUBLICATION-LIMITS, CONTINUITY AND DIFFERENTIABILITY-QUESTION BANK
  1. lim(x rarr oo) ((x^(2) + 5x + 3)/(x^(2) + x + 2))^(x) is :

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  2. For x in R, lim(x rarr oo) ((x-3)/(x+2))^(x) is equal to :

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  3. The value of lim(n rarr oo) (1 + 2^(4) + 3^(4) +…...+n^(4))/(n^(5)) - ...

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  4. lim(x rarr 0) (log (3 + x) - log(3 - x))/(x) = k, the value of k is :

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  5. The value of lim(x rarr 0) (int(0)^(x^(2))sec^(2)t dt)/(x sin x) is :

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  6. lim(x rarr (pi)/(2)) ((1 - tan x//2)(1-sin x))/((1+tan x//2) (pi - 2x)...

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  7. If lim(h rarr 0) (1 + (a)/(x) + (b)/(x^(2)))^(2x) = e^(2), then the va...

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  8. Let alpha and beta be the distinct roots of ax^(2) + bx + c = 0, then ...

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  9. Let a = lim(n rarr oo) (1+2+3+.....+n)/(n^(2))=, b = lim(n rarr oo) (...

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  10. If a,b, c, d are positive, then lim(x rarr oo) (1 + 1/(a+bx))^(c+dx)=

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  11. lim(x rarr 0) (a^(x)-b^(x))/x =

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  12. lim(x rarr 1) (sqrt(x-1) + sqrt(x-1))/(sqrt(x^(2)-1)) =

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  13. lim(x rarr 0) x/(sqrt(x+4)-2) =

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  14. lim(x rarr 0) [[(log(1+x))]/x]=

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  15. lim(x rarr oo)((a^(1/x)+b^(1/x)+c^(1/x))/3)^x, where a, b, c are real ...

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  16. lim(x rarr oo) ((2x+7sinx)/(4x+3cosx)) =

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  17. lim(x rarr 0) (log (1+x))/(3^(x) - 1)=

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  18. lim(theta rarr pi/2) (1-sin theta )/((pi/2 - theta) cos theta)=

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  19. lim(x rarr 0) (x.10^(x)-x)/(1-cos x) =

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  20. lim(x rarr oo) ((x+a)/(x+b))^(x+b) =

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