Home
Class 12
MATHS
If y=x+(1)/(x+(1)/(x+(1)/(x+...oo)))," p...

If `y=x+(1)/(x+(1)/(x+(1)/(x+...oo)))," prove that "(dy)/(dx)=(y)/((2y-x)).`

Text Solution

AI Generated Solution

To solve the problem, we need to differentiate the equation \( y = x + \frac{1}{x + \frac{1}{x + \frac{1}{x + \ldots}}} \) and prove that \( \frac{dy}{dx} = \frac{y}{2y - x} \). ### Step-by-Step Solution: 1. **Define the Infinite Series**: We start with the equation: \[ y = x + \frac{1}{y} ...
Promotional Banner

Topper's Solved these Questions

  • DIFFERENTIATION

    RS AGGARWAL|Exercise Exercise 10H|10 Videos

  • DIFFERENTIATION

    RS AGGARWAL|Exercise Exercise 10I|51 Videos

  • DIFFERENTIATION

    RS AGGARWAL|Exercise Exercise 10F|66 Videos

  • DIFFERENTIAL EQUATIONS WITH VARIABLE SEPARABLE

    RS AGGARWAL|Exercise Exercise 19B|60 Videos

  • FUNCTIONS

    RS AGGARWAL|Exercise Exercise 2D|11 Videos

Similar Questions

Explore conceptually related problems

If y=x+(1)/(x+(1)/((1)/(x+...))), prove that(dy)/(dx)=(y)/(2y-x)

If y=x+(1)/(x+(1)/(x+(1)/(x+1))), prove that (dy)/(dx)=(y)/(2y-x)

If y=x+(1)/(x+(1)/(x+(1)/(x+))), prove that (dy)/(dx)=(y)/(2y-x)

If y=(1)/(x+(1)/(x+(1)/(x+...*+oo))) prove that (1+y^(2))(dy)/(dx)+y^(2)=0

If y =x+(1)/(x +(1)/(x+.....oo)) then prove that xdy/dx =y/(2y -x).

If ye^(y)=x, prove that,(dy)/(dx)=(y)/(x(1+y))

If y=log(x+(1)/(x)), prove that (dy)/(dx)=(x-1)/(2x(x+1))

If y = x + (1)/(x + (1)/( x +...oo)) then (dy)/(dx) =

If y=(x)/(x+2), prove that x(dy)/(dx)=(1-y)y

If y=x+1/(x+1/(x+1/(x+.....))), prove that (dy)/(dx)=1/(2-x/(x+1/(x+1/(x+...))))