Home
Class 12
MATHS
If x=a(1-cos^3theta) , y=a\ sin^3theta ,...

If `x=a(1-cos^3theta)` , `y=a\ sin^3theta` , prove that `(d^2y)/(dx^2)=(32)/(27\ a)` at `theta=pi/6` .

Text Solution

AI Generated Solution

Promotional Banner

Topper's Solved these Questions

  • FUNCTION

    RD SHARMA ENGLISH|Exercise All Questions|406 Videos
  • INCREASING AND DECREASING FUNCTION

    RD SHARMA ENGLISH|Exercise All Questions|232 Videos

Similar Questions

Explore conceptually related problems

If x=a(1-cos^3theta),y=asin^3theta,"prove that"(d^2y)/(dx^2)=(32)/(27a) "at" theta=pi/6dot

If x=a(1+costheta) , y=a(theta+sintheta) , prove that (d^2y)/(dx^2)=(-1)/a at theta=pi/2 .

If x=a(1-costheta) , y=a(theta+sintheta) , prove that (d^2y)/(dx^2)=-1/a at theta=pi/2 .

If x=acos^3theta,y=a sin^3theta then find (d^2y)/(dx^(2))

If x=costheta , y=s in^3theta , prove that y\ (d^2y)/(dx^2)+((dy)/(dx))^2=3\ s in^2theta(5\ cos^2theta-1) .

If x=acos^3theta,y=a sin^3theta, then find the value of d2y/dx2 at θ=π/6

If x=acos^3theta and y=asin^3theta, then find the value of (d^2y)/(dx^2) at theta=pi/6dot

If x=acos^3theta and y=asin^3theta, then find the value of (d^2y)/(dx^2) at theta=pi/6dot

If x=costheta,y=sin^3theta,"prove that" y(d^2y)/(dx^2)+((dy)/(dx))^2=3sin^2theta(5cos^2theta-1)dot

If x = a cos^(3) theta, y = a sin ^(3) theta then sqrt(1+((dy)/(dx))^(2)) =?

RD SHARMA ENGLISH-HIGHER ORDER DERIVATIVES-All Questions
  1. If y=e^xcosx , prove that (d^2y)/(dx^2)=2\ e^xcos(x+pi/2) .

    Text Solution

    |

  2. If x=acostheta , y=bsintheta , show that (d^2y)/(dx^2)=-(b^4)/(a^2y^3)...

    Text Solution

    |

  3. If x=a(1-cos^3theta) , y=a\ sin^3theta , prove that (d^2y)/(dx^2)=(32)...

    Text Solution

    |

  4. If x=a(theta+sintheta) , y=a(1+costheta) , prove that (d^2y)/(dx^2)=-a...

    Text Solution

    |

  5. If x=a(theta-sintheta) , y=a(1+costheta) find (d^2y)/(dx^2)

    Text Solution

    |

  6. If x=a(1-costheta) , y=a(theta+sintheta) , prove that (d^2y)/(dx^2)=-1...

    Text Solution

    |

  7. If x=a(1+costheta) , y=a(theta+sintheta) , prove that (d^2y)/(dx^2)=(-...

    Text Solution

    |

  8. If x=costheta , y=s in^3theta , prove that y\ (d^2y)/(dx^2)+((dy)/(dx)...

    Text Solution

    |

  9. If y=sin(sinx) , prove that (d^2y)/(dx^2)+tanxdot(dy)/(dx)+y\ cos^2x=0...

    Text Solution

    |

  10. If x=sint ,y=sinpt, prove that (1-x^2)(d^2y)/(dx^2)-x(dy)/(dx)+p^2y...

    Text Solution

    |

  11. If y=(sin^(-1)x)^2 , prove that (1-x^2)y2-x y1-2=0 .

    Text Solution

    |

  12. If y=e^(tan^(-1)x) , prove that (1+x^2)y2+(2x-1)y1=0 .

    Text Solution

    |

  13. If y=3cos(logx)+4sin(logx),\ prove that x^2y2+x\ y1+y=0 .

    Text Solution

    |

  14. If y=e^(2x)(a x+b) , show that y2-4\ y1+4\ y=0 .

    Text Solution

    |

  15. If x=sin(1/alogy) , show that (1-x^2)y2-x\ y1-a^2\ y=0 .

    Text Solution

    |

  16. If logy=tan^(-1)x , show that (1+x^2)y2+(2x-1)y1=0 .

    Text Solution

    |

  17. If y=tan^(-1)x , show that (1+x^2)(d^2y)/(dx^2)+2x(dy)/(dx)=0 .

    Text Solution

    |

  18. If y={log(x+sqrt(x^2+1))}^2 , show that (1+x^2)(d^2y)/(dx^2)+x(dy)/(dx...

    Text Solution

    |

  19. If y=(tan^(-1)x)^2 , then prove that (1+x^2)^2\ y2+2x\ (1+x^2)y1=2 .

    Text Solution

    |

  20. If y=cotx show that (d^2y)/(dx^2)+2y(dy)/(dx)=0 .

    Text Solution

    |