Problem 4. Let LC R³ be the lower hemispherc, i.c. FOLLO ALLE = {(x, y, z) | x² + y² + z² = 1 and z≤ 0}. Let DCR³ be the closed disk in the xy-plane, i.e., D = {(x, y,0) | x² + y² ≤ 1}. a for a homegmarah for f-15 9.0 NM J a. Give an explicit expression for wolle homeomorphism f: L→ D. b. Give an explicit expression for f-¹.

Q: 1. Identify each of the following subsets of the Euclidean plane R2 as open set or closed set or…

A: Explanation of the answer is as follows. As per the rules I am doing first three sub parts in…

Q: 3. [For students with ID # ending in 4 or 5.] Through the point (4, 2, -5) and perpendicular to the…

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Q: 3) A vector is given as A = x(z+2)â,-()x+1)â, +(y+2)â. Prove the Stoke's theorem for the geometry…

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Q: 22Prove that the line X2l+2t y=ー+3t そ2 :2+4t is s perpendicular tou the plane X-2yrzz6

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Q: Find the distance from y to the plane in R spanned by the set {u1, uz} 4 - 3 -3 y = -9 -4 Uz 2 4 1…

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Q: Show that set : A = {(x,y) = R² : sin(x) ≤ y ≤ 2e-2²] is closed on Euclidean plane R².

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Q: 5. Among all the points on the graph of z = 10 – x² – y² that lie above the plane r+2y +3z = 0, find…

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Q: 3. Determine the intersection (if any) of the following planes. Show your work clearly ₁: 2x + 3y z…

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Q: The distance between the point P(x₁, y₁, 2₁) to the plone with equation Ax+By+ (z+D=0 is equal to |…

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Q: Find the points on the sphere x² + y° + z?=1. that are closest to and farthest from the point (2, 1,…

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Q: The space curve 7(t) = (t, t, t) is known as the twisted cubic and it is shown below: Match each…

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Q: 2. Find the volume of the parallelepiped the following 3 vectors describe the edges: i.q=i-2j-3k, b=…

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Q: II1. Recall that using vector projections, we showed that the dis- tance from a point (x1, Y1, 21)…

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Q: 3.Compute ((x + y)² + z² + 2yz)dS, where Σ is the sphere f x² + y² + z² = 2x + 2z.

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Q: Apply Gauss's theorem to evaluate. A

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Q: (d) Let (Fn) be a sequence of closed subsets of M, and S, (j = 1,...,5) be subsets of M such that.…

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Q: 9. Suppose that a : R³ → R³ by perpendicular projection onto the plane 3x – 2y + z = 0. Find ↑

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Q: Show that (Cod) is metric space

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