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underset( x rarr 0 ) ("Lim") [ ((1+x)^(1...

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

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The correct Answer is:
`e^(-(1)/(2))`
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MOTION-LIMIT-EXERCISE-3
  1. underset( x rarr oo)("Lim")[cos (2pi ((x)/(1+ x ))^(a))]^(x^(2))a in Q

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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  20. evaluate lim(x->a)1/((a^2-x^2)^2)((a^2+x^2)/(a x)-2sin((api)/2)sin((pi...

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