3 Problem 5: Fuller proofs are expected for these. (a) What is the area of the largest rectangle that fits inside of the ellipse x2+2y = 1? I include a figure below, for those possibly unfamiliar with conic sections. (b) Prove the following: Let c e (a, b). Iff is continuous on [a, bl, differentiable on (a, b), and limgc f(x)=L, then f'(c) L Figure for 5(a). 0.5 I I 0 nU I I -0.5 1 0.5 0 -0.5 -1 IX

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Q: 2 Find pxV 1+ 3x² dr, where P is the ellipse parametrized as follows: r(t) = , 0<t< 2n

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A: We will find the asymptotes of the hyperbola.Below find the solution in the image.

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Q: z2 – x² – y2 = 1 %3D -

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