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Most Important Selected Qs for JEE AdvancedMathematicsApplication of Derivatives

Paragraph: If y= _ u(x) ^ v(x) f(t) d t , let us define d y d x in a different manner as d y d x =v^ (x) f^2(v(x))-u^ (x) f^2(u(x)) and the equation of the tangent at (a, b) as y-b= ( d y d x )_ (a, b) (x-a) Question: If y= _x^ x^2 t^2 d t , then equation of tangent at x=1 is

Options

  1. Ay=x+1
  2. Bx+y=1
  3. Cy=x-1
  4. Dy=x

Correct answer

C. y=x-1

Step-by-step solution

At x=1, y=0 d y d x =2 x (x^4 )^2- (x^2 )^2=2-1=1 Equation of tangent y -0=1( x -1), y = x -1

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