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If y=sin(mcos^(-1)x) then prove that (1-...

If `y`=`sin(mcos^(-1)x)` then prove that `(1-x^(2))y_(2)-xy_(1)+m^(2)y=0`.

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MODERN PUBLICATION-CONTINUITY AND DIFFERENTIABILITY-PROBLEM
  1. sinx=2t/1+t^(2), tany=2t/1-t^(2), find dy/dx.

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  2. Find dy/dx, x=3 cos t-2cos^3t, y=3sint-2sin^3t.

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  3. If y=sin(mcos^(-1)x) then prove that (1-x^(2))y(2)-xy(1)+m^(2)y=0.

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  4. If y=cos^(-1)((2cosx-3sinx)/sqrt13), then find dy/dx.

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  5. Examine the continuity of the following functions at indicated points....

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  6. Show that f(x)={(x sin frac{1}{x}, xne0),(o,x=0):} is continuous at x...

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  7. Prove that e^x-2=0 has a solution between 0 and 1.

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  8. So that x^5+x+1=0 for some value of x between -1 and 0.

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  9. Examine continuity and differentiability f(x)={[(1-e^(-x))/x,x!=0],[1,...

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  10. If x=2costheta-cos2theta , y= 2sintheta-sin2theta then find d^(2)y/dx^...

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  11. If y =(sin^(-1) x)^2, prove that (1-x^2)y2 - xy1 - 2 = 0

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  12. Find dy/dx for the following . y=log(2)sqrtsinphi(x).

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  13. Find dy/dx if (x/a)^(2/3) + (y/b)^(2/3) = 1

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  14. Find dy/dx if y = x cot^(-1) (x/y)

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  15. Find dy/dx if (cosx)^(y)=(siny)^(x)

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  16. Find (dy)/(dx), if y=tan^(-1)((cosx)/(1+sinx)).

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  17. Find dy/dx if e^(3x)In(sin2x)+e^sqrtcosx.

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  18. Differentiate tan^(-1) ((1+sinx)/(1-sinx))^(1/2) w.r.t. log((1+cosx)/(...

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  19. Find dy/dx y=tan^(-1)(xsinalpha-xcosalpha)

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  20. Find dy/dx y = cos^(-1)(1-1/x-1/x^(2))^(1/2)

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