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MHT CET2007MathematicsApplication of Derivatives

The slope of the tangent at (x, y) to a curve passing through (1, 4 ) is given by y x - ² ( y x ) , then the equation of the curve is

Options

  1. Ay= ⁻¹ [ ( e x ) ]
  2. By=x ⁻¹ [ ( x e ) ]
  3. Cy=x ⁻¹ [ ( e x ) ]
  4. DNone of the above

Correct answer

C. y=x ⁻¹ [ ( e x ) ]

Step-by-step solution

According to the given condition, d y d x = y x - ² ( y x ) On putting y=v x d y d x =v+x d v d x , we get aligned & v+x d v d x =v- ² v & d v ² v =- d x x & ² v d v= -1 x d x aligned On integrating both sides, we get v=- x+ c ( y x )=- x+ c Since, this curve is passing through (1, / 4) . array l ( 4 )=- 1+ c c=1 ( y x )=- x+1 ( y x )=- x+ e y=x ⁻¹ [ ( e x ) ] array

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