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Integral Calcul...

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  • Question 1
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    Consider the function f(x) = x2 –x –2. The maximum value of f(x) in the closed interval [–4, 4] is  

  • Question 2
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  • Question 3
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  • Question 4
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    The function f(x,y) = 2x2 +2xy –y3 has  

  • Question 5
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    Equation of the line normal to function f(x) = (x-8)2/3 +1 at P(0,5) is  

  • Question 6
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    The distance between the origin and the point nearest to it on the surface z2 = 1 + xy is  

  • Question 7
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    Given a function  

    The optimal value of f(x, y)

  • Question 8
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    For the function f(x) = x2 e-x, the maximum occurs when x is equal to  

  • Question 9
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    A cubic polynomial with real coefficients  

  • Question 10
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    Given y = x2 + 2x + 10, the value of  

  • Question 11
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    Consider the function y = x2 –6x + 9. The maximum value of y obtained when x varies over the interval 2 to 5 is  

  • Question 12
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  • Question 13
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    The magnitude of the gradient of the function f = xyz3 at (1,0,2) is  

  • Question 14
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    The expression curl (grad f), where f is a scalar function, is  

  • Question 15
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    If the velocity vector in a two –dimensional flow field is given by     the  vorticity vector, curl   

  • Question 16
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    The vector field  

  • Question 17
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    The angle between two unit-magnitude co-planar vectors P (0.866, 0.500, 0) and Q (0.259, 0.966, 0) will be  

  • Question 18
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    Stokes theorem connects  

  • Question 19
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  • Question 20
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    If   then  is

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