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Evaluate the following limit: lim(n->oo)...

Evaluate the following limit: `lim_(n->oo)(1/(n^2)+2/(n^2)+3/(n^2)++(n-1)/(n^2\ ))`

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`lim_(x->infty) (1/(n^2)+2/(n^2)+3/(n^2)+ldots+(n-1)/(n^2\ ))`
`= lim_(x->infty) 1/n^2(1+2+3+ldots+(n-1))`
`=lim_(x->infty) 1/n^2{(n-1)n}/2`
`=lim_(x->infty) 1/n^2 xx {n^2(1-1/n)}/2`
`=lim_(x->infty)1/2(1-1/n)`
`=1/2`
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RD SHARMA-LIMITS-All Questions
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  2. Evaluate the following limit: lim(n->oo){sqrt(x+1)-sqrt(x)}sqrt(x+2)

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  3. Evaluate the following limit: lim(n->oo)(1/(n^2)+2/(n^2)+3/(n^2)++(n-1...

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  4. Evaluate the following limit: lim(n->oo)(1^3+2^3+ n^3)/((n-1)^4)

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  5. lim(x->oo)(x^4+7x^3+46 x+a)/(x^4+6) where a is a non-zero real number.

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  6. Evaluate the following limit: lim(x->-oo)(sqrt(x^2-8x)+x)

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  7. Evaluate the following limit: lim(x->oo)(sqrt(x^2+a^2)-sqrt(x^2+b^2))/...

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  8. lim(n->oo)(1^2+2^2+3^2+..........+n^2)/n^3

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  9. lim(n->oo)(1^2+2^2+3^2+..........+n^2)/n^3

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  10. Evaluate the following limit: lim(x->0)(x^2)/(sin x^2)

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  11. Evaluate the following limit: lim(x->0)(sinxcosx)/(3x)

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  12. Evaluate the following limit: lim(x->0)(3sin x-4sin^3x)/x

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  13. lim(x->0)(tanm x)/(tann x)

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  14. Evaluate the following limit: (lim)(x->0)(sinx^0)/(x^0)

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  15. Evaluate the following limit: (lim)(x->0)(cos a x-cos b x)/(cosc x-cos...

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  16. Evaluate the following limit: (lim)(x->0)(1-cosm x)/(x^2)

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  17. Evaluate the following limit: (lim)(x->0)(cos3x-cos7x)/(x^2)

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  18. Evaluate the following limit: (lim)(x->0)(xcosx+2\ sin x)/(x^2+tanx)

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  19. Evaluate the following limit: (lim)(x->0)(5xcosx+3sinx)/(3x^2+tanx)

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  20. Evaluate the following limit: (lim)(x->0)(sin5x-sin3x)/(sinx)

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