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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 F(x)= ^x e^ t^2 / 2 (1-t^2 ) d t , then d d x F(x) at x=1 is

Options

  1. A0
  2. B-1
  3. C1
  4. D2

Correct answer

A. 0

Step-by-step solution

F(x)= ₁^x e^ t^2 / 2 (1-t^2 ) d tF^ (x)= (e^ x^2 2 (1-x^2 ) )^2 F^ (1)=e^ 1 / 2 0=0

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