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Evaluate: underset(nrarrinfty)lim[(1/n^2...

Evaluate: `underset(nrarrinfty)lim[(1/n^2sec^2(1/(n^2))+2/n^2sec^2((4)/(n^2))....+1/nsec^2(1)]`

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`(3sqrt3)/(2pi)`
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PATHFINDER-DEFINITE INTEGRATION-QUESTION BANK
  1. underset(trarra)lim(inta^tf(x)dx-((t-a)/2)(f(t)-f(a)))/(t-a)^3

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  2. Evaluate :underset(nrarrinfty)lim((1^m+2^m+...+n^m)/n^(m+1))

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  3. Evaluate: underset(nrarrinfty)lim[(1/n^2sec^2(1/(n^2))+2/n^2sec^2((4)/...

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  4. The value of underset(nrarrinfty)limn{1/(3n^2+8n+4)+1/(3n^2+16n+16)+.....

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  5. The value of underset(nrarrinfty)lim1/n^2{sin^3(pi)/(4n)+2sin^3 (2pi)/...

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  6. The value of (n!)/((n-2)!) ia

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  7. The value of int(-2)^2 (sin^2x)/([x/pi]+1/2) dx where [x] denotes the ...

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  8. If I=int(pi/6)^(pi/6) (pi+4x^5)/(1-sin(absx+pi/6))dx then I equals

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  9. I=int(-2)^2(abs(1-x^4))dx then I equals

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  10. I=int-1^1([x^2]+log((2+x)/(2-x))dx....(1) where [x] denotes the greate...

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  11. if f(x) is a function such that f(x+k)=f(x) for K in I^+ and I=int0^k...

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  12. let T le0 be a fixed real number suppose f is continuous function such...

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  13. ifI=int0^(pi/2)( sin8xlog(cotx))/(cos2x)dx then I equals

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  14. ifI=int(1/3)^3 1/xsin (1/x-x)dx then I equals

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  15. if b gt a and I=inta^b dx/(sqrt((x-a)(b-x) then I equals

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  16. if I=int0^(pi/2) dx/(5+3sinx)=lambdatan^(-1)(1/2) then value oflambda ...

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  17. if I=int(1/e)^e abslogx dx/x^2 then I equals

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  18. The natural number nle5 for which In=int0^1 e^x(x-1)^n dx=16-6e is

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  19. ifI=int0^a sqrt((a-x)/(a+x))dx, agt0 Then I equals

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  20. Evaluate: int0^(pi/2)sin^3x cosxdx

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