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Let L = lim (n to oo) (((2.1+n))/(1^(2)+...

Let `L = lim _(n to oo) (((2.1+n))/(1^(2)+n .1 +n^(2))+((2.2+n))/(2 ^(2)+n.2+n^(2))+((2.3+n))/(3 ^(2) +n.3 +n^(2))+ ...... + ((2.n +n))/(3n^(2)))` then value of `e ^(L)` is:

A

2

B

3

C

4

D

`3/2`

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Verified by Experts

The correct Answer is:
B
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VK JAISWAL ENGLISH-INDEFINITE AND DEFINITE INTEGRATION-EXERCISE (SUBJECTIVE TYPE PROBLEMS)
  1. Let L = lim (n to oo) (((2.1+n))/(1^(2)+n .1 +n^(2))+((2.2+n))/(2 ^(2)...

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  2. int (x+ ( cos^(-1)3x )^(2))/(sqrt(1-9x ^(2)))dx = (1)/(k (1)) ( sqrt(1...

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  3. If int (0)^(oo) (x ^(3))/((a ^(2)+ x ^(2)))dx = (1)/(ka ^(6)), then fi...

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  4. int( (x^2+1)dx)/x

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  5. If int (x ^(6) +x ^(4)+x^(2)) sqrt(2x ^(4) +3x ^(2)+6) dx = ((ax ^(6) ...

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  6. int( x^2+3)/(x^2+2)dx

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  7. The value of int (tan x )/(tan ^(2) x + tan x+1)dx =x -(2)/(sqrtA) tan...

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  9. Let int ( 1) ^(sqrt5)(x ^(2x ^(2)+1) +ln "("x ^(2x ^(2x ^(2+1)))")")dx...

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  10. If int (dx )/(cos ^(3) x-sin ^(3))=A tan ^(-1) (f (x)) +bln |(sqrt2+f ...

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  11. Find the value of |a| for which the area of triangle included between ...

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  12. Let I = int (0) ^(pi) x ^(6) (pi-x) ^(8)dx, then (pi ^(15))/((""^(15) ...

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  13. int( x^3)/(x^2-3)dx

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  14. If a continuous function f on [0,a] satisfies f(x)f(a-x)=1,agt0, then ...

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  20. The maximum value of int (-pi/2) ^((3pi)/2) sin x. f (x) dx, subject t...

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  21. Given a function g, continous everywhere such that g (1)=5 and int (0)...

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