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Evaluate: ("lim")(nvec0)8/(x^8){1-cos(x^...

Evaluate: `("lim")_(nvec0)8/(x^8){1-cos(x^2)/2-cos(x^2)/4+cos(x^2)/2cos(x^2)/4}`

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BANSAL-CONTINUITY AND DIFFERENTIABILITY-All Questions
  1. (lim)(xvec-7)([x]^2+15[x]+56)/("sin"(x+7)"sin"(x+8))= (where [.] denot...

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  2. Evaluate the following limit: (lim)(x->(3pi)/4)(1-tan3x)/(1-2cos^2x)

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  3. Evaluate: ("lim")(nvec0)8/(x^8){1-cos(x^2)/2-cos(x^2)/4+cos(x^2)/2cos(...

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  4. Evaluate the limit: ("lim")(xvec1)(sumk=1 100 x^k-100)/(x-1)

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  5. Evaluate the following limit: (lim)(x->1)(x^3+x^2-2)/("sin"(x-1))

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  6. Evaluate the limit if exists, lim(x->1)[{ln(1+x)-ln2}{3.4^[x-1]-3x}]...

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  7. The value of ("lim")(xvec1)(p/(1-x^p)-q/(1-x^q)),p ,q , in N , equal ...

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  8. let {an},{bn},{cn} be sequences such that (1) an+bn+cn=2n+1 , (2) anbn...

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  9. 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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  10. Let L=prod(n=3)^oo (1-4/n^2); M=prod(n=2)^oo ((n^3-1)/(n^3+1)) and N=p...

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  11. If l = lim(a-> oo) sum(r=2)^a [ (r+1) sin (pi/(r+1)) - r sin (pi/r...

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  12. underset( xrarr oo )("Lim")x^(2) sin(lnsqrt( cos ""( pi)/( x)))

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

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

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

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

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

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

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

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