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Find lim(ntooo)(1/(n+1)+1/(n+2)+...+1/(...

Find
`lim_(ntooo)(1/(n+1)+1/(n+2)+...+1/(6n))`

A

log 2

B

log 3

C

log 6

D

0

Text Solution

Verified by Experts

The correct Answer is:
C
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Show tha , lim_(ntooo) ((1)/( n +1)+(1)/( n +2)+ . . . +(1)/( 6 n))= log 6 .

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MARVEL PUBLICATION-INTEGRATION - DEFINITE INTEGRALS -MULTIPLE CHOICE QUESTIONS (PART - B : Mastering The BEST)
  1. The integral underset(0)overset(a)int (g(x))/(f(x)+f(a-x))dx vanishes...

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  2. If I(n)=underset(0)overset(pi//4)inttan^(n)x dx, then (1)/(I(2)+I(4)...

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  3. The value int(-2)^(2) (plog ((1+x)/(1-x)) + q log ((1-x)/(1+x))^(-2) +...

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  4. lim(n to oo)((sum(r=1)^(n)r^(2))(sum(r=1)^(n)r^(3)))/((sum(r=1)^(n)r^(...

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  5. If : int(0)^(pi)ln(sin x) dx = k, then : int(0)^(pi//4)ln (1+tan x)=

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  6. int(pi/3)^(pi/2) sqrt(1+cosx)/(1-cosx)^(5/2) dx

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  7. int(-pi//2)^(pi//2)(sin^(2)x.cos^(2)x(sin x+cos x))dx=

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  8. If : int(ln 2)^(x)(1)/(sqrt(e^(t)-1))dt=(pi)/(6), then : x =

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  9. int(0)^(pi//2)sin x.cos x. sqrt(a^(2).sin^(2)x+b^(2).cos^(2)x)dx=

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  10. If int0^oo (x^2 \ dx)/((x^2+a^2)(x^2+b^2)(x^2+c^2)) = pi/(2(a+b)(b+c)(...

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  11. int(0)^(2) (2x-2)/(2x-x^(2)) dx is equal to

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  12. int(1)^(e^(99))(sin(pi.ln x))/(x)dx=

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  13. Evaluate : lim(n-> oo) (1^4+2^4+3^4+...+n^4)/n^5 - lim(n->oo) (1^3+2^3...

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  14. int(0) ^(pi//2) ((sin x +cos x )^(2))/sqrt(1+ sin 2x)dx =

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  15. The value of int(8 log(1+x))/(1+x^(2)) dx is

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  16. Find lim(ntooo)(1/(n+1)+1/(n+2)+...+1/(6n))

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  17. (x.sin^(-1)x^(2))/(sqrt(1-x^(4)))

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  18. overset(2pi) underset(0)int(xsin^(2n)x)/(sin^(2n)x+cos^(2n)x)dx,n gt 0...

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  19. If f(x)=Asin((pix)/2)+B, f'(1/2)=sqrt2 and int0^1 f(x)dx=(2A)/pi then ...

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  20. int(pi//4)^(3pi//4)(dx)/(1+cos x)=

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