Home
Class 12
MATHS
If x=2a t , y=a t^2 , where a is a const...

If `x=2a t` , `y=a t^2` , where `a` is a constant, then find `(d^2y)/(dx^2)` at `x=1/2`

Text Solution

AI Generated Solution

To find \(\frac{d^2y}{dx^2}\) at \(x = \frac{1}{2}\), we will follow these steps: ### Step 1: Express \(y\) in terms of \(t\) Given: \[ y = at^2 \] ...
Promotional Banner

Topper's Solved these Questions

  • FUNCTION

    RD SHARMA|Exercise Solved Examples And Exercises|393 Videos

  • INCREASING AND DECREASING FUNCTION

    RD SHARMA|Exercise Solved Examples And Exercises|232 Videos

Similar Questions

Explore conceptually related problems

If x=a(t-sint), y=a(1-cost) then find (d^2y)/(dx^2) .

If t=(x^(4)+cotx), find (d^(2)y)/(dx^(2)) .

If x=a(cos t+t sin t) and y=a(sin t-t cos t), then find (d^(2)y)/(dx^(2))

If x=3cos t and y=5sint , where t is a parameter, then 9(d^(2)y)/(dx^(2)) at t=-(pi)/(6) is equal to

If y = sin t and x = 2 t then (d^(2)y)/(dx^(2)) =

If x=tlogt,y=t^(t)," then "(d^2y)/(dx^(2))=

If x=a sin t and y=a(cos t+(log tan t)/(2)) find (d^(2)y)/(dx^(2))

If x=a(cos2t+2t sin2t) and y=a(sin2t-2t cos2t), then find (d^(2)y)/(dx^(2))

If x=a sin t and y=a(cos t+log tan(t)/(2)) find (d^(2)y)/(dx^(2))

RD SHARMA-HIGHER ORDER DERIVATIVES-Solved Examples And Exercises
  1. If x=acosn t-bsinn t and (d^2x)/(dt^2)=lambdax , then find the value ...

    Text Solution

    |

  2. If x=t^2 and y=t^3 , find (d^2y)/(dx^2) .

    Text Solution

    |

  3. If x=2a t , y=a t^2 , where a is a constant, then find (d^2y)/(dx^2...

    Text Solution

    |

  4. If x=f(t) and y=g(t) , then write the value of (d^2y)/(dx^2) .

    Text Solution

    |

  5. If y=1-x+(x^2)/(2!)-(x^3)/(3!)+(x^4)/(4!)...... oo , then write (d^2y)...

    Text Solution

    |

  6. If y=x+e^x , find (d^2x)/(dy^2) .

    Text Solution

    |

  7. If y=|x-x^2| , then find (d^2y)/(dx^2) .

    Text Solution

    |

  8. If y=|(log)e x| , find (d^2y)/(dx^2) .

    Text Solution

    |

  9. If x=acosnt-bsinnt , then (d^2x)/(dt^2) is (a)n^2x (b) -n^2x (c) n x ...

    Text Solution

    |

  10. If x=a t^2,\ \ y=2\ a t , then (d^2y)/(dx^2)= -1/(t^2) (b) 1/(2\ a t^...

    Text Solution

    |

  11. If y=a x^(n+1)+b x^(-n) , then x^2(d^2y)/(dx^2)= (a)n(n-1)y (b) n(n+1...

    Text Solution

    |

  12. (d^(20))/(dx^(20))(2cosxcos3x)= 2^(20)(cos2x-2^(20)cos4x) (b) 2^(20)(...

    Text Solution

    |

  13. If x=t^2,\ \ y=t^3 , then (d^2y)/(dx^2)= (a)3//2 (b) 3//4t (c) 3//2t ...

    Text Solution

    |

  14. If y=a+b x^2,\ a ,\ b arbitrary constants, then (d^2y)/(dx^2)=2\ x y...

    Text Solution

    |

  15. If f(x)=(cosx+isinx)(cos2x+isin2x)(cos3x+isin3x)ddot(cosn x+isinn x) a...

    Text Solution

    |

  16. If y=asinm x+bcosm x , then (d^2y)/(dx^2) is equal to (a)-m^2y (b) m^2...

    Text Solution

    |

  17. If f(x)=(sin^(-1)x)/(sqrt(1-x^2)),t h e n(1-x^2)f^(x)-xf(x)= 1 (b) ...

    Text Solution

    |

  18. If y=tan^(-1){((log)e(e//x^2))/((log)e(e x^2))}+tan^(-1)((3+2\ (log)e ...

    Text Solution

    |

  19. Let f(x) be a polynomial. Then, the second order derivative of f(e^...

    Text Solution

    |

  20. If y=acos((log)e x)+bsin((log)e x) , then x^2\ y2+x y1= (a) 0 (b) y (...

    Text Solution

    |