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If x=a(cos 2 theta+2 theta sin 2 theta) ...

If `x=a(cos 2 theta+2 theta sin 2 theta) " and" y=a(sin 2 theta - 2 theta cos 2 theta)`, find `(d^(2)y)/(dx^(2)) " at" theta =(pi)/(8)`.

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Verified by Experts

The correct Answer is:
`(8sqrt2)/(pia)`
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MODERN PUBLICATION-CONTINUITY AND DIFFERENTIABILITY-EXERCISE 5(k) (LONG ANSWER TYPE QUESTIONS (I))
  1. If x=cost+logtant/2,\ \ y=sint , then find the value of (d^2y)/(dt^2) ...

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  2. Find (d^(2)y)/(dx^(2)) when : x=2costheta-cos2thetaandy=2sintheta-si...

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  3. If x=a(cos 2 theta+2 theta sin 2 theta) " and" y=a(sin 2 theta - 2 the...

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  4. If x=asint\ and y=a(cost+logtant/2) , find (d^2\ y)/(dx^2)

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  5. If x+y=tan^(-1)y" and "(d^(2)y)/(dx^(2))=f(y)(dy)/(dx), then f(y)=

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  6. If y=(sin^(-1)x)^2 then prove that (1-x^(2))(d^2y)/(dx^2)-x(dy)/(dx)-2...

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  7. If y=(cos^(-1)x)^(2), then prove that : (1-x^(2))y(2)-xy(1)-2=0.

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  8. If y=(tan^(-1)x)^2, show that (x^2+1)^2y2+2x(x^2+1)y1=2

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  9. If y=(cot^(-1)x)^(2), then show that (x^(2)+1)^(2)(d^(2)y)/(dx^(2))+2x...

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  10. If y=(s in^(-1)\ x)/(sqrt(1-x^2)) , show that (1-x^2) (d^2\ y)/(dx^2)...

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  11. If y=log\ [x+sqrt(x^2+1)] , prove that (x^2+1)(d^2\ y)/(dx^2)+x(dy)/(d...

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  12. If y=log{x+sqrt(x^2+a^2)} , prove that: (x^2+a^2)(d^2y)/(dx^2)+x(dy)/(...

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  13. If y={x +sqrt(x^(2)+1)}^(m), then show that (x^(2)+1)(d^(2)y)/(dx^(2))...

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  14. If y=cos(mcos^(-1)x), then prove that : (1-x^(2))(d^(2)y)/(dx^(2))-x...

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  15. If y=sin(mtan^(-1)x), prove that : (1+x^(2))^(2)y(2)+2x(1+x^(2))y(1)...

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  16. If y=e^(msin^(-1)x),-1lexle1, show that : (1-x^(2))y(2)-xy(1)-m^(2)y...

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  17. If y=e^(acos^(-1)x),-1lexle1, show that : dy/dx=(-ae^(acos^(-1)x))/(sq...

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  18. If y=e^acos^((-1)x),-1lt=xlt=1,show that (1-x^2)(d^2y)/(dx^2)-x(dy)/(d...

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  19. If y=e^(mtan^(-1)x), prove that : (1+x^(2))(d^(2)y)/(dx^(2))+(2x-m)d...

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  20. If y=e^(ax)cosbx, then prove that : (d^(2)y)/(dx^(2))-2ady/dx+(a^(2)...

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