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the value of lim(n->oo) {1/(n^3+1)+4/(n^...

the value of `lim_(n->oo) {1/(n^3+1)+4/(n^3+1)+9/(n^3+1)+.................+n^2/(n^3+1)}`

A

1

B

`2//3`

C

`1//3`

D

`0`

Text Solution

Verified by Experts

The correct Answer is:
C
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VMC MODULES ENGLISH-DIFFERENTIAL CALCULUS-LEVEL 2
  1. lim(xto oo)(x/(1+x))^(x) is

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  2. If 0 lt alpha lt beta then underset(n to oo)(lim) (beta^(n) + alpha^(n...

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  3. the value of lim(n->oo) {1/(n^3+1)+4/(n^3+1)+9/(n^3+1)+..................

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  4. lim(n to oo)sum(r=1)^(n)cot^(-1)(r^(2)+3//4) is (a) 0 (b) tan^(-1)1 (...

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  5. Evaluateunderset(xto pi//4)lim(2-tanx)^(1//1n(tanx))

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  6. underset(xrarr(pi)/(4))(lim)(int(2)^(sec^(2)x)f(t)dt)/(x^(2-)(pi^(2))/...

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  7. lim(x->0)(x^4(cot^4x-cot^2x+1)/(tan^4x-tan^2x+1)) is equal to (a) 1 (...

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  8. lim(xto0)((e^(x)-1)/x)^(1//x)

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  9. If [.] denotes the greatest integer function then lim(x->oo)([x]+[2x]...

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  10. ("lim")(xvecoo)((x^2+2x-1)/(2x^2-3x-2))^((2x+1)/(2x-1))i se q u a lto ...

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  11. lim(x to oo) (( 1+x+x^(3)))/((ln x)^(3)) is equal to

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  12. int cot^6x cosec^2xdx

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  13. underset(xtooo)lim(e^(1//x^(2))-1)/(2tan^(-1)(x^(2))-pi) is equal to

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  14. lim(x->0) ((1+x)^(1/x)-e)/x is equal to

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  15. lim(xto0)(((1+x)^(1//x))/e)^(1/(sinx)) is equal to

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  16. lim(x->-oo)(x^5tan(1/(pix^2))+3|x^2|+7)/(|x^3|+7|x|+8) is equal to: a....

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  17. Let f(x)=3x^10-7x^8+5x^6-21x^3+3x^2-7 , then the value of lim(h->0)...

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  18. lim(x->a){[(a^(1/2)+x^(1/2))/(a^(1/4)-x^(1/4)))^(- 1)-(2(a x)^(1/4))/(...

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  19. lim(xto1) (sum(r=1)^(n)x^(r)-n)/(x-1) is equal to

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  20. Evaluate: ("lim")(n→oo)x[tan^(-1)((x+1)/(x+2))-tan^(-1)(x/(x+2))]

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