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Evaluate ("Lim")(x->0)[1/(x^2)-1/(sin^2x...

Evaluate `("Lim")_(x->0)[1/(x^2)-1/(sin^2x)]` using LHospitals Rule or otherwise :

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BANSAL-LIMITS AND DERIVATIVES-All Questions
  1. If f(x)=|"cos"(x+x^2)"sin"(x+x^2)-"cos"(x+x^2)"sin"(x-x^2)"cos"(x-x^2...

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  2. Let alpha be a repeated root of a quadratic equation f(x)=0a n dA(x...

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  3. Evaluate ("Lim")(x->0)[1/(x^2)-1/(sin^2x)] using LHospitals Rule or ot...

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  4. Evaluate ("Lim")(x->0)(1+sinx-cosx+ln(1-x))/(x tan^2x) using LHospital...

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  5. If ("Lim")(x->0)(asinx-b x+c x^2+x^3)/(2x^2dotln(1+x)-2x^3+x^4) exists...

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  6. Evaluate: ("Lim")(x->0)(x^(6000)-(sinx)^(6000))/(x^2dot(sinx)^(6000))

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  7. If lim(x->0)(1-cosx.cos2x.cos3x ....cosn x)/x^2 has the value equal to...

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  8. Find the value of ("Lim")(x->0)(1-cos^5xcos^3 2xcos^3 3x)/(x^2)

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  9. If ln(x+y)=2x y , then y '(0)?

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  10. f(x)={bsin^-1((x+c)/2),-1/2 lt xlt0 and 1/2 , x=0 and e^(((ax)/2)-1)/...

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  11. If y=y(x) and it follows the relation xcosy+ycosx=pi then y''(0) is

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  12. Let S denote the set of all polynomials P(x) of degree lt=2 such th...

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  13. If f(x) is a continuous and differentiable function and f(1/n) = 0 ...

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  14. The value of lim(x->0)((sinx)^(1/x)+(1/x)^(sinx)) , where x >0, is ...

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  15. (d^2x)/(dy^2) equals: (1) ((d^2y)/(dx^2))^(-1) (2) -((d^2y)/(dx^2...

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  16. Let g(x)=logf(x),w h e r ef(x) is a twice differentiable positive func...

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  17. Let f and g be real valued functions defined on interval (-1,\ 1) such...

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  18. If the function f(x)=x^3+e^(x/2) and g(x)=f^(-1)(x), then the value of...

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  19. Let f(theta)=sin(tan^(-1)((sintheta)/(sqrt(cos2theta)))),w h e r e-p...

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  20. Let y be an implicit function of x defined by x^(2x)-2x^xcot y-1=0....

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