12) Prove Ñ' (t) are Smooth space for any always orthogonal (*+€ dom Ŕ³). that Curve R(t), 7(t) and

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A: First, we will find the equation of a line given two points.

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A: Use the formula for the Euclidean distance and distance along the curve .

Q: Please don't provide handwritten solution .... ) Consider the space R^2 equipped with the sunflower…

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A: Assume that f(z) is analytic on the unit disk D ={z: |z| < 1}.Also assume that |f(z)|≤1 for…

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Q: -3. 3) to the curve given by f(x) =

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Q: d set): Let (M ,d) be a (SUT)' = S' U T'.

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Q: 6) (From Hardcover Book, Marsden/Tromba, Vector Calculus, 6th ed., Section 4.1., # 20) Show that, at…

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A: Summary:At a hyperbolic point on a surface, the Gaussian curvature is negative, indicating that the…

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Q: dependent.

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Q: Show that in 3D space, (a) k EijkEpqk = δip&jq – διαδjp

A: Note:  Since you have posted multiple questions, we will solve first question for you. Kindly repost…

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A: Let's see the method of integration. We use residue method to solve this integral.

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A: We will find out the required length.

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A: The two given planes are x-y+z=0 and x+y+2z=0.

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Q: 6. (a) Show that the curve represented by the vector function F(t) = (5t, 3t – 4, 2t² – 6) is at the…

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