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Evaluate: (lim)(x->0)log(tan^2x)(tan^...

Evaluate: `(lim)_(x->0)log_(tan^2x)(tan^2 2x)dot`

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BANSAL-CONTINUITY AND DIFFERENTIABILITY-All Questions
  1. (lim)(x->oo)(x/(1+x))^x

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  2. (lim)(x->oo)((2tan^(-1)x)/pi)^x

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  3. Evaluate: (lim)(x->0)log(tan^2x)(tan^2 2x)dot

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  4. Evaluate: lim(x->0)x^m(logx)^n ,m , n in Ndot

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  5. Evaluate: ("lim")(xvec0)(sin^(-1)x-tan^(-1)x)/(x^3)

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  6. f(x)=(lim)(n->oo)(t a npix^2+(x+1)^n s in x)/(x^2+(x+1)^n) , find (...

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  7. f(x)=(lim)(n->oo)(cospix-x^(2n)"sin"(x-1))/(1+x^(2n+1)-x^(2n)) , fi...

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  8. Evaluate (lim)(x->0)(1+tan^2sqrt(x))^(1//x)

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  9. (lim)(x->tan^(-1)3)([tan^3x]-2[t a n x]-3)/([tan^2x]-4[tanx]+3) (where...

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  10. Evaluate of the following limit: (lim)(x->0)(e^x-1-x)/(x^2)

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  11. Evaluate of the following limit: (lim)(x->0)(x-sinx)/(x^3)

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

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  13. Evaluate of the following limit: (lim)(x->0)(x-t a n x)/(x^3)

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  14. Evaluate: (lim)(x->0)(e^x-1-x^3)/(sin^6 2x)

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  15. The value of lim(xto0) ((1+x)^(1//x)-e)/(x) is

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  16. If (lim)(x->0)(A cos x+B xsinx-5)/(x^4) exists & finite. Find A\ &\...

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  17. if f(x)=(4+sin2x+Asinx+Bcosx)/x^2 for x!=0 is continuous at x=0 then A...

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  18. Evaluate the following : (lim)(x->0)(e^x^2-cosx)/(x^2)

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  19. Evaluate the following limit: (lim)(x->0)(e^(s in2x)-e^(sin\ x))/x

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

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