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

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

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BANSAL-CONTINUITY AND DIFFERENTIABILITY-All Questions
  1. Evaluate of the following limit: (lim)(x->0)(e^x-e^(-x)-2x)/(x^3)

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

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

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

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

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

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

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

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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. Find the points of discontinuity of the following function f(x)=1/(2...

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  11. Find the points of discontinuity of the following function f(x)=x^2...

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  12. Find the points of discontinuity of the function: f(x)=1/(x^4+x^2+1)

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  13. Find the points of discontinuity of the function: f(x)=1/(1-e^((x-1)/(...

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  14. f(x)=[(cos x)cot^2x!=0e^(-1//2)\ if\ x=0 find whether the f(x) is cont...

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  15. The function f(x) = {x+asqrt2 sinx, 0<=x<=pi/4 and 2x cotx+b, pi/4<=x...

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  16. Sketch the graph of the following function f(x)=|ln|x||

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  17. The function f:""R""~""{0}vecR given by f(x)=1/x-2/(e^(2x)-1) ca...

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  18. Let f(x)={(1+3x)^(1/x),x!=0e^3,x=0dotD i s c u s st h econ t inu i t y...

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  19. Which of the following functions is not continuous AAx in R ? sqrt(2...

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  20. Discuss the continuity of f(x)={(x^4-5x^2+4)/(|(x-1)(x-2)|),x!=1,2, 6...

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