MTH 301 Calculus II Assignment No 2 Solution Ideas Spring 2014

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[SIZE="4"][B]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.

(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.[/B]

[Vuhelper]

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)