Home
Class 12
MATHS
If y=sqrt(x+sqrt(x+sqrt(x+ tooo))) , t...

If `y=sqrt(x+sqrt(x+sqrt(x+ tooo)))` , then `(dy)/(dx)` is equal to.....

A

`x/(2y-1)`

B

`2/(2y-1)`

C

`-1/(2y-1)`

D

`1/(2y-1)`

Text Solution

Verified by Experts

The correct Answer is:
D
Given `y=sqrt(x+sqrt(x+sqrt(x+…..oo)))`
`impliesy=sqrt(x+y)`
On squaring both sides, we get
`y^(2)=x+yimplies2y(dy)/(dx)=1+(dy)/(dx)`
`implies(dy)/(dx)(2y-1)=1implies(dy)/(dx)=1/(2y-1)`
Promotional Banner

Topper's Solved these Questions

  • PRACTICE SET 07

    MHTCET PREVIOUS YEAR PAPERS AND PRACTICE PAPERS|Exercise PAPER 2( MATHEMATICS)|50 Videos

  • PRACTICE SET 09

    MHTCET PREVIOUS YEAR PAPERS AND PRACTICE PAPERS|Exercise PAPER 2 (MATHEMATICS)|50 Videos

Similar Questions

Explore conceptually related problems

If y=sqrt(x+sqrt(x+sqrt(x.." to "oo)))," then "(dy)/(dx)=

Let y=sqrt(x+sqrt(x+sqrt(x+...oo)))," then "(dy)/(dx) is equal to

If y=sqrt(x+sqrt(y+sqrt(x+sqrt(y+...oo)))) , then (dy)/(dx) is equal to

If y= sqrt (x+ sqrt (x+ sqrt (x))),then (dy)/(dx) =

If y= sqrt(cos x) + sqrt (cos sqrt (x)),then (dy)/(dx)

If x=sqrt(y+sqrt(y+sqrt(y+..."to"oo)))," then: "(dy)/(dx)=

If y=e^(sqrt(x))+e^(-sqrt(x))," then "(dy)/(dx) is equal to

If y= log (sqrt(x - 1)) - sqrt(x + 1)) , "then " (dy)/(dx) is equal to

if y=sqrt(x) + 1/sqrt(x) , then (dy)/(dx) at x=1 is equal to

MHTCET PREVIOUS YEAR PAPERS AND PRACTICE PAPERS-PRACTICE SET 08-PAPER 2 OBJECTIVE TYPE
  1. ~(p vv q)vv (~p ^^ q) is logically equivalent to

    Text Solution

    |

  2. The line x=2y intersects the ellipse (x^(2))/4+y^(2)=1 at the points P...

    Text Solution

    |

  3. The equation of tangent of y^(2)=12x and making an angle (pi)/3 with X...

    Text Solution

    |

  4. If sin(x+3 alpha)=3sin (alpha-x) then

    Text Solution

    |

  5. The distance of the mid -point of line joining two ponts (4,0) and (0,...

    Text Solution

    |

  6. The locus of the point from which the length of the tangent to the cir...

    Text Solution

    |

  7. If the function f(x)=x^(3)-6x^(2)+ax+b satisfies Rolle's theorem in t...

    Text Solution

    |

  8. If y=sqrt(x+sqrt(x+sqrt(x+ tooo))) , then (dy)/(dx) is equal to.....

    Text Solution

    |

  9. If A=[(2,-1),(-1,2)] and l is the unit matrix of order 2, then A^(2) e...

    Text Solution

    |

  10. If two dice are thrown simultaneously then probability that 1 comes on...

    Text Solution

    |

  11. The value of f at x =0 so that funcation f(x) = (2^(x) -2^(-x))/x , ...

    Text Solution

    |

  12. Let p and q be two statements. Then, (~p vv q) ^^ (~p ^^ ~q) is a

    Text Solution

    |

  13. The function f(x)=2x^(3)-3x^(2)-12x-4 has

    Text Solution

    |

  14. int(0)^(1)(x^(7))/(sqrt(1-x^(4)))dx is equal to

    Text Solution

    |

  15. If x^(y)=e^(x-y), then (dy)/(dx) is equal to

    Text Solution

    |

  16. The value of a.a' is

    Text Solution

    |

  17. If a plane meets the coordinate axes at A,B and C such that the centro...

    Text Solution

    |

  18. Minimise z=3x+y, subject to 2x+3yle6,x+yge1, xge0,yge0

    Text Solution

    |

  19. A paticle acted on by constant forces 4hati=hatj-3hatk and 3hati+hatj-...

    Text Solution

    |

  20. Solution of the differential equation tan y.sec^(2) x dx + tan x. sec^...

    Text Solution

    |