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If x =sin t,y = sin 2t then prove that (...

If x =sin t,y = sin 2t then prove that `(1-x^2)(d^2y)/(dx^2)- x dy/dx + 4y = 0`

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(i) If x=sin t , y=sin 2t then prove that (1-x^2)d^2y/dx^2-xdy/dx+4y=0 . If y=gof (x) then find dy/dx.

(i) if x=sint , y= sinpt , then show that (1-x^2) d^2 y/dx^2 - x dy/dx +p^2 y =0 . Br Determine the differentials of z=cos 2t -2 cot t .

If x = sint and y= sin (pt) , then show that (1-x^(2) ) (d^2y)/( dx^2) - x (dy)/( dx) + p^(2) y =0 .

If x=cos theta and y=sin 5 theta , then prove that (1-x^(2))(d^(2)y)/(dx^(2))-x(dy)/(dx)+25y=0

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If y=e^(x)sinx , then prove that (d^(2)y)/(dx^(2))-2(dy)/(dx)+2y=0 ,

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MODERN PUBLICATION-CONTINUITY AND DIFFERENTIABILITY-PROBLEM
  1. Prove that e^x-2=0 has a solution between 0 and 1.

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

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

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

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

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

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

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

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

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

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

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

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

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

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  15. Find dy/dx x=cos^(3)t/sqrtcos2t, y=sin^(3)t/sqrt cos2t

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  16. If x =sin t,y = sin 2t then prove that (1-x^2)(d^2y)/(dx^2)- x dy/dx +...

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  17. If y = e^(m cos^(-1) x) (1-x^2)y2-xy1 = m^2y

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  18. Differentiate y=tan^(-1).(sqrt(1+x^(2))+sqrt(1-x^(2)))/(sqrt(1+x^(2))-...

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  19. If sqrt(1-x^4) + sqrt(1-y^4) =k(x^2 - y^2) then show that dy/dx = {x...

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  20. If x = (1-cos^2 theta)/(cos theta), y = (1-cos^(2n)theta)/(cos^n theta...

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