2) Let R' real numbers, define < x,y>= x,Y1 + 3x2y; + 5x3y3 for x = (x, X2, X3) and y (y,Yz, Y3). Is < x,y> inner product c

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A: We know that, The sum of distances to any point on the ellipse x,y from the two foci c,0 and -c,0 is…

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A: 2d graph of  x = z^2

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Q: 3 K find OXA Curd A) at

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Q: 9. Show that the function (-, -) : IR² × R² → IR defined by setting = #1#2 + 2x12 + 2y1*2 + 8y1Y2 /2…

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Q: a) F(x,y, z) : planes x = 0, x = 1, y = 0, y = 1, z = 0, and z = 1. 3xi + xyj + 2xzk and E is the…

A: Solution of (a) is in given below

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Q: 17. Integrate G(x, y, z) = xyz over the triangular surface with vertices (1, 0, 0), (0, 2, 0), and…

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Q: Let UsX +Sinx Deter of X 0n [0,)where ļ Find . derivalire fa 2x+1 x²+7 te tn 6x+

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A: W need to find elements which are invertible inZ4x,y.

Q: Verify the Cauchy-Schwarz Inequality for u = (1, −1, 3) and v = (2, 0, −1).

A: u = (1, −1, 3) and v = (2, 0, −1) To verify the Cauchy-Schwartz Inequality for the given set of…

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A: The standard form of the equation of the hyperbola is,

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Q: 5. Evaluate f (x²zdx – yx²dy + 3dz) where C is the boundary of the triangle with vertices (0,0, 0),…

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Q: Differentiate, and make sure to show all your work: y = exin(2z) %3D

A: The given question is taken from the derivative of the function in which we have to find the…

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Q: Cannot solve

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Q: Let C be the curve which is the union of two line segments, the first going from (0, 0) to (3, 2)…

A: C be the curve point (0,0) to (3,2) and (3,2) to (6,0) so, integral we need to compute I =∫c3dy-2dxI…

Q: (ii) Verify Cauchy-Goursat theorem for f(z) = 5 sin 2z if C is the square with vertices at 1土も-1土。

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Q: Bounded by the cylinders z = 2x2, y = x² and the planes z = 0, y = 4

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Q: t in 30 minute please duopoly with homogeneous goods. There ar

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Q: Let C be the line segment from point (0, 1, 1) to point (2, 2, 3). Evaluate line integral yds. C

A: To evaluate the line integral

Q: The solid bounded by y = 4, z = x², z = 2y, and z = 4.

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Q: Show that the line integral 22 +2ry) dx + x? dy + 2xz dz, is independent of path in R, where C runs…

A: We will find out the required values.

Q: 11. Circle in the plane z = 1 with center (3, 2) and passing through the origin.

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Q: How would I solve ∭xzdV, where E is bounded by the planes z = 0, z=y, and the cylinder x2 + y2 = 1…

A: The given equation of the cylinder us x2+y2=1 in the half space y≥0. Calculate the value of ∫∫∫xzdV,…

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Q: Show that 1 y - X 1. Z-y X-Z = 1. %3D alx-y) alz - x)

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Q: Find the surfaces on which the function u = 2 (x2 + y²)/z is constar

A: Since u is a constant so, x2+y2z=4a , where a is an arbitrary constant.

Q: 4. Let f(x, y, z) = e² + zy² and let C be a straight line segment connecting the points (4,2,1) and…

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Q: 8. Evaluate the double integral // ydrdy where T is the triangle with vertices (0,-1), (0,5), (4,…

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Q: Evaluate the line integralf, (xy + z)ds along the line segment C from (1,2,3) to (-1,1,5).

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Q: Evaluate the line integral §. xy²dx + 2x²y dy over triangular path with vertices (0,0), (2,2) and…

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Q: Evaluate the line integral x²z ds, where C is the line segment from (0,6, 2) to (8, 5, 1).

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Q: Show that I1fll= 1 forthe functional of 7be aLineur funct i'onal on X de fined by fcx)=

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Q: (x, y) = x¹ 3 1 0 120 001 y, x, y = R³

A: The function &lt;x,y&gt; will be inner product if  1) Non negetivity: &lt;x,x&gt; ≥ 0, for all x and…

Q: Let C be the curve which is the union of two line segments, the first going from (0, 0) to (-1, -2)…

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Q: Prove that the integral: √ [2xyz² dx + (x²z² + z cos yz)dy + (2x²yz + y cos yz)dz ] Is independent…

A: The given integral is ∫C2xyz2dx+x2z2+zcos yzdy+2x2yz+y cos yzdz. The objective is to prove that the…