# How do you find the circumference of the ellipse #x^2+4y^2=1#?

Using numerical techniques, we can get a approximation for this as:

# C = 4.8442 #

Although this seems like quite a simple question, the answer is actually ridiculous complicated.

We need to first put the ellipse equation in standard form:

Comparing with the standard equation;

Then the exact circumference is given by:

Using numerical techniques, we can get a approximation for this as:

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To find the circumference of the ellipse (x^2 + 4y^2 = 1), you can use the following formula:

[ C = 4aE(e) ]

where (a) is the semi-major axis, (b) is the semi-minor axis, and (e) is the eccentricity of the ellipse. In this ellipse, since it's of the form (x^2/a^2 + y^2/b^2 = 1), the semi-major axis (a) is (1) (since (a) corresponds to the term with (x^2)) and the semi-minor axis (b) is (\frac{1}{2}) (since (b) corresponds to the term with (y^2)).

To find (e), the eccentricity, use the formula:

[ e = \sqrt{1 - \frac{b^2}{a^2}} ]

Substitute the values of (a) and (b) into the formula to find (e). Then, plug in (a) and (e) into the formula (C = 4aE(e)) to get the circumference of the ellipse.

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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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