1. Let X R². For any (x1, y1), (2, y2) E R², define d₂((x1, y₁), (x2, y2)) := Show that d₂ is a metric on R². /(x₂-x₁)² + (y₂ - Y₁)².

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

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A: The natural point that comes in our mind is (2,6).

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Q: For the z-coordinate of the north pole at N(11,9,12), how did you guys get 12?

A: Your question is why maximum value of z is 12?  I show this in two ways. Geometrically Analytically

Q: Evaluate [[ 4.ry² — 5x + 5y³ dA over the rectangle R = {(x, y) : -1 ≤ x ≤ 2 and − 1 ≤ y ≤1}.

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Q: If f(x,y,z) = x2 + y2, what is the locus of points in space for which grad f is parallel to the…

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Q: Find B and t for the space curve r(t) = N 11 ਕਰਜ |·+|· 1 +1 + 2 3 ()+( 3 +1 j, t> 0.

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Q: 2. Prove that if d is a metric for X, then another metric d' for X is given by if a ≤ b " if b ≤ a…

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Q: 1. Find all points on the graph of h(x, y) = plane is horizontal. 3x²9x + 4 + 2y³ - 12y where the…

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Q: Use the distance formula to show that T (x,y) = (-y,x) is an isometry.

A: We have to prove that T(x, y) = (-y, x) is an isometric.

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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Q: Let de(x, y) := |x — y|, d₁(x,y) := for x,y E R. Show that (a) d₁ is a metric on R; (b) dẼ and d₁…

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Q: For X = (x₁,...,xn), Y = (y₁, ..., Yn) € Rn, define n d(X,Y) := Σ |xi - vi| i=1 (a). Show that d is…

A: Given that, are two vectors.The defined function is: To check the d is matrix space on , have to…

Q: Let f(x, y) = x2 − 2y and g(x, y) = xey . Show that at any point (x0, y0), the level curve of f…

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Q: Let C be the curve in the x-y plane defined by the equation (x – h) + v – k)* =? where h, k, and r…

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Q: Find dyldx for the following equation: 2x+ y -9y+9=0. A) dy dx 2-2y В) dy dx 9-2y 2 C) dy dx 9-у 1…

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