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(lim)(x->0)[((1+x)^(1//x))/e]^(1//x)\ \...

`(lim)_(x->0)[((1+x)^(1//x))/e]^(1//x)\ \ `

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BANSAL-CONTINUITY AND DIFFERENTIABILITY-All Questions
  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. (lim)(x->0)[((1+x)^(1//x))/e]^(1//x)\ \

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  4. Evaluate : lim[x->oo](x/e-x(x/[x+1])^x)

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  5. Let x0=2(cos)pi/6and xn=sqrt(2+x(n-1)).n=1,2,3,....... find Lim(n->oo)...

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  6. if f(x) = lim(n->oo) 2/n^2(sum(k=1)^n kx)((3^(nx)-1)/(3^(nx)+1)) where...

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  7. Let f(x)=lim(n rarr oo)(2x^(2n)sin\ 1/x+x)/(1+x^(2n)) then find (a) li...

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  8. Let f(x)=lim(n rarr oo)(2x^(2n)sin\ 1/x+x)/(1+x^(2n)) then find (a) li...

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  9. Let f(x)=lim(n->oo)(2x^(2n)sin(1/x)+x)/(1+x^(2n)) then find (a) lim...

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  10. Let f(x)=(lim)(n->oo)(2x^(2n)sin1/x+x)/(1+x^(2n))\ then find :\ (lim)...

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  11. Through a point A on a circle, a chord AP is drawn & on the tangent at...

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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. Let (lim)(x->1)(x^6+1+5/3(x^4+x^2)-8/3(x^5+x))/(x^5+x+6x^3-4x^4-4x^2)=...

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  15. Let lim(x->oo)xln(e(1+1/x)^(1-x)) equal m/n where m and n are relati...

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  16. Find the value of a for which the following function is continuous ...

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  17. Find the value of a for which the following function is continuous ...

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  18. Find the value of a for which the following function is continuous a...

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  19. Find the value of a for which the following function is continuous ...

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  20. Find the value of a for which the following function is continuous a...

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