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lim(x->-oo)((3x^4+2x^2)sin(1/x)+|x|^3+5)...

`lim_(x->-oo)((3x^4+2x^2)sin(1/x)+|x|^3+5)/(|x|^3+|x|^2+|x|+1)`

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BANSAL-CONTINUITY AND DIFFERENTIABILITY-All Questions
  1. Evaluate the following limits: lim(xto0)(sin4x)/(6x)

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  2. Evaluate the following limit: (lim)(x->0)(e ^(x^2)-3^(3x))/(sin((x^2...

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  3. lim(x->-oo)((3x^4+2x^2)sin(1/x)+|x|^3+5)/(|x|^3+|x|^2+|x|+1)

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  4. Evaluate the following limit: (lim)(x->1/(sqrt(2)))(cos^(-1)(2xsqrt...

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  5. (lim)(xvec-7)([x]^2+15[x]+56)/("sin"(x+7)"sin"(x+8))= (where [.] denot...

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

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

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

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

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

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

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

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  13. 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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  14. 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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  15. If l = lim(a-> oo) sum(r=2)^a [ (r+1) sin (pi/(r+1)) - r sin (pi/r...

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

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

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

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

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

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