a) What is the area of the largest rectangle that fits inside of the ellipse

b) Prove the following: Let c in (a, b). If f is continuous on

Elleanor Mckenzie
2021-02-25
Answered

Prove these examples are correct:

a) What is the area of the largest rectangle that fits inside of the ellipse

${x}^{2}\text{}+\text{}2{y}^{2}=1?$

b) Prove the following: Let c in (a, b). If f is continuous on$[a,\text{}b],$ differentiable on (a, b)?

a) What is the area of the largest rectangle that fits inside of the ellipse

b) Prove the following: Let c in (a, b). If f is continuous on

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Velsenw

Answered 2021-02-26
Author has **91** answers

a) Сonsider this figure:

From the figure it can be seen that:

Area

And also,

We've taken the positive value since we chose this point to be in the first quadrant

So now deciding:

Differentiating the above function with respect to "y":

For maximize the area:

Put,

Corresponding to this,

Hence the maximum area:

Area

b)Prove the following: Let c in (a, b). If f is continuous on [a, b], differentiable on (a, b), and:

Properties used

Proof is given below:

Since:

By using the property:

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