3. Let d₂(x, y) = |arctan(x) — arctan(y)| for x, y € R. (a) Show that d₂ is a metric on R. (b) Are de and d₂ equivalent?

Q: 3. Use implicit differentiation to find əz - for ?х x²+2y²+5z²=2.

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A: We use line integration to evaluate this.

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Q: Consider the space curve r(t) = (cost cos 2t, cost sin 2t, sin t). (a) Find r(t).

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Q: 1. Calculate y³ $ £ (-2² - sinz) dz + ( + v) ds. + dx dy, 3 3 where C is the circle of radius 1…

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