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

`lim_(n->oo) ((sqrt(n^2+n)-1)/n)^(2sqrt(n^2+n)-1)`

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The correct Answer is:
`e^(-1)`
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The value of lim_(nrarroo) ((sqrtn^(2)+n-1)/(n))^(2sqrt(n^(2)+n-1)) is

lim_(nrarroo)((1)/(sqrt(n^(2)))+(1)/(sqrt(n^(2)-1^(2)))+(1)/(sqrt(n^(2)-2^(2)))+....+(1)/(sqrt(n^(2)-(n-1)^(2)))) is equal to

lim_(n rarr oo)(sqrt(n^(2)+n)-sqrt(n^2+1))

lim_ (n rarr oo) ((sqrt (n ^ (2) + n) -1) / (n)) ^ (2sqrt (n ^ (2) + n) -1)

lim_(n rarr oo)(1)/(sqrt(n^(2)))+(1)/(sqrt(n^(2)+1))+(1)/(sqrt(n^(2) +2))+...(.1)/(sqrt(n^(2)+2n))=

The value of lim_(nto oo)(1/(sqrt(n^(2)))+1/(sqrt(n^(2)+1))+…..+1/(sqrt(n^(2)+2n))) is

The value of lim_(n rarr oo)(sqrt(3n^(2)-1)-sqrt(2n^(2)-1))/(4n+3) is

The value of lim_(n rarr oo)(1/sqrt(4n^(2)-1)+1/sqrt(4n^(2)-4)+...+1/sqrt(4n^(2)-n^(2))) is -

lim_(nto oo)1/n+(1)/(sqrt(n^(2)+n))+(1)/(sqrt(n^(2)+2n))+...(1)/(sqrt(n^(2)+(n-1)n)) is equal to

lim_ (n-> oo) (sqrt (n))/(sqrt (n)+sqrt (n+1)) = (i) 1 (ii) 1/2 (iii) 0 (iv) infty

MOTION-LIMIT-EXERCISE-3
  1. underset( x rarr 0 ) ( "Lim") ((x- 1+ cos x )/( x))^((1)/( x))

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  2. underset( x rarr oo)("Lim")[cos (2pi ((x)/(1+ x ))^(a))]^(x^(2))a in Q

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

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  4. underset( x rarr 0 ) ("Lim") [ ((1+x)^(1//x))/( e ) ]^(1//x)

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  5. underset( x rarr oo) ("Lim") ((cos h ( pi //x))/(cos( pi//x)))^(x^(2))

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  6. Evaluate lim(x->1)(root13 x- root 7 x)/(root5 x- root3 x)

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  7. lim[x->1] ([sum[k=1]^100x^k]-100])/(x-1)

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  8. lim(x ->oo)x^(2)(sqrt((x+2)/(x))-root(3)((x+3)/(x))) equals

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  9. A circular are of radius 1 subtends an angle of x radians 0 < x < pi/2...

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  10. A circular are of radius 1 subtends an angle of x radians 0 < x < pi/2...

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  11. A circular are of radius 1 subtends an angle of x radians 0 < x < pi/2...

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  12. At the end points A,B of the fixed segment of length L, lines are draw...

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  13. At the endpoint and midpoint of a circular are AB, tangent lines are ...

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  14. lim(x->0) [ ln(1+sin^2x) cot ln^2(1+x)]

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  15. lim(x->oo)(a(2x^3-x^2)+b(x^3+5x^2-1)-c(3x^3+x^2))/(2(5x^4-x)-b x^4+c(4...

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  16. find a&b if lim(x->oo) ((x^2+1)/(x+1)-ax-b)=0

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  17. lim(x rarr oo) (sqrt(x^2-x+1)-a x-b)=0, then a+b=

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  18. lim(x->0)[lim(x->oo)(e x p(xln(1+(a y)/x))-e x p(x In(1+(b y)/x)))/y]

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  19. underset( x rarr 1) ( "Lim") ( tan "" ( pi x)/( 4))^(tan""( pix)/( 2))

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  20. Let f(x)=(sin^-1(1-{x})*cos^-1(1-{x}))/(sqrt(2{x})(1-{x})), then find ...

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