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Evaluate lim(n->oo)n[1/((n+1)(n+2))+1/((...

Evaluate `lim_(n->oo)n[1/((n+1)(n+2))+1/((n+2)(n+4))+....+1/(6n^2)]`

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CENGAGE PUBLICATION-INTEGRALS-All Questions
  1. Evaluate: lim(n->oo)[1/(n a)+1/(n a+1)+1/(n a+2)++1/(n b)]

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  2. int0^x|sint|dt, where x in (2npi,(2n+1)pi),ninN,is equal to (A) 4n...

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  3. Evaluate lim(n->oo)n[1/((n+1)(n+2))+1/((n+2)(n+4))+....+1/(6n^2)]

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  4. Let f be an odd continous function which is periodic with priod 2 if g...

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  5. Evaluate inta^b(dx)/(sqrt(x)),w h e r ea , b > 0.

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  6. Let f: R to R and g: R to R be continuous function. Then the value of ...

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  7. Evaluate: int(-(3pi)/2)^(-pi/2)[(x+pi)^3+cos^2(x+3pi)]dx

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  8. Evaluate: int0^(1/2)(xsin^(-1)x)/(sqrt(1-x^2))dx

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  9. Evaluate: int0^(100)x-[x]dx where [dot] represents the greatest in...

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  10. If Sn=[1/(1+sqrt(n))+1/(2+sqrt(2n))+....+1/(n+sqrt(n^2))] then (lim)(n...

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  11. The value of ("lim")(nvecoo)sum(r=1)^(4n)(sqrt(n))/(sqrt(r)(3sqrt(r)+s...

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  12. The value of (int0^n[x]dx)/(int0^n{x}dx is (where [x] and {x} denotes ...

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  13. Evaluate: int(-pi/4)^(npi-pi/4)|sinx+cosx|dx

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  14. The value of int0^(pi/2)dx/(1+tan^3x) is

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  15. Evaluate: int(-pi)^pi(1-x^2)sinxcos^2xdx

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  16. Let f be a contiuous function on [a,b]. If F(x)=(int(a)^(x)f(t)dt-int(...

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  17. Evaluate the following: int(-1)^(1)(sin x-x^(2))/(3-|x|)dx

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  18. If int(a)^(b)|sinx|dx=8 and int(0)^(a+b)|cosx|dx=9, then find the valu...

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  19. Evaluate: int(-pi/2)^(pi/2)sqrt(cos^(2n-1)x-cos^(2n+1)x)dx ,w h e r en...

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  20. f(x) is a continuous and bijective function on Rdot If AAt in R , the...

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