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12th Standard English Medium Maths Subject Differentials and Partial Derivatives Book Back 2 Mark Questions with Solution Part - II

12th Standard

    Reg.No. :
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Maths

Time : 01:00:00 Hrs
Total Marks : 10

    2 Marks

    5 x 2 = 10
  1. Find df for f(x) = x2 + 3x and evaluate it for
    x = 2 and dx = 0.1

  2. If U(x, y, z) = \(\frac { { x }^{ 2 }+{ y }^{ 2 } }{ xy } +3{ z }^{ 2 }y\), find \(\frac { \partial U }{ \partial x } ;\frac { \partial U }{ \partial y } \) and \(\frac { \partial U }{ \partial z } \)

  3. If w(x, y, z) = x2 y + y2z + z2x, x, y, z∈R, find the differential dw .

  4. In each of the following cases, determine whether the following function is homogeneous or not. If it is so, find the degree.
    \(U(x,y,z)=xy+sin\left( \frac { { y }^{ 2 }-2{ x }^{ 2 } }{ xy } \right) \)

  5. Show that F(x,y) = \(\frac { { x }^{ 2 }+5xy-10{ y }^{ 2 } }{ 3x+7y } \) is a homogeneous function of degree 1.

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