User:Egm6341.s10.Team4.roni/HW7/7.10

= Problem 10: Parameterization of an Ellipse =

Given
Result from HW problem 7.9 [[media:Egm6341.s10.mtg42.djvu|42-1]], which is:

$$\displaystyle Eq. (1)  \qquad    \frac{x^2}{a^2}+ \frac{y^2}{b^2}=1 $$

Show
That the arc length dl comes to:

HW 7.10 on slide [[media:Egm6341.s10.mtg42.djvu|42-2]]

$$\displaystyle

Eq. (2) \qquad  dl= \sqrt{dx^2+dy^2} $$

Solution
Geometrically:


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Eq. (3) \qquad  dl^2= {dx^2+dy^2} $$



Eq. (4) \qquad  dl=  \sqrt{dx^2+dy^2} $$

and also:



Eq. (5) \qquad  dl =   \left( \sqrt{1+  \left( \frac{dy}{dx}\right)^2} \right) dx

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$$\displaystyle dl= \sqrt{dx^2+dy^2} $$
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Author
Solved and typed by - Egm6341.s10.Team4.roni 18:50, 18 April 2010 (UTC) Reviewed by -