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Thread: MTH 301 Calculus II Assignment No 2 Solution Ideas Spring 2014

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    MTH 301 Calculus II Assignment No 2 Solution Ideas Spring 2014

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    MTH 301 Calculus II Assignment No 2 Solution Ideas Spring 2014

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    Symmetry about the Initial Line

    If the equation of a curve remains unchanged when (r,θ)
    is replaced by either (r,-θ) in its equation ,then the curve
    is symmetric about initial line.

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    (ii) Symmetry about the y-axis

    If when (r, θ) is replaced by either (r,π θ − ) in
    The equation of a curve and an equivalent equation
    is obtained ,then the curve is symmetric about the
    line perpendicular to the initial i.e, the y-axis

    (ii) Symmetry about the Pole

    If the equation of a curve remains unchanged

    when either (-r, θ) or is substituted for (r, θ)
    in its equation ,then the curve is symmetric
    about the pole. In such a case ,the center of
    the curve.

  2. #2
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    Suppose vertices are O(0,0),A(2,0),B(2,2)

    For interior points with respect to x:

    f(x)=(3x^2)-3y (a)

    Interior points with respect y:

    f(y)3-3x (b)

    for the boundary points we take on the segment OA

    y=0

    U(x)=f(x,0)=x^3

    Regarded as function of x denied on the closed interval (2<=x<=2) its extreme value may be occur at the end point x=2 and so on which corresponded to the point (2,0) and (2,2)

    U’(x)=3x^2=0

    On segment OB x=0 and V(y)=(0,y)=3y

    Using symmetric form possible points are also these (0,0)(2,0)(2,2)

    The interior point of AB y=2-x

    Fy=x^3+3(2-x)-3x(2-x)

    Fy=(x^3)-3(x^2)-9x+6

    Take derivative

    Fy’=3x^2-7x





    Points are (2,2)


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