Let P be the portion of the tilted plane in R' parameterised by r(u, v) = ui + uj + vk where 0 < x < 1 and 0 < z < 1. To calculate the area of P we can use Area(P) = |J(u, v)| dv du. u=0 Jv=0 Here the Jacobian |J(u, v)| is ...

Q: Let z = g(z, y) = f(3 cos(ry), y + e") provided that f(3, 7) = 4, fi(3, 7) = 2, f2(3, 7) = 3. i)…

A: Let z=gx,y=f3cosxy, y+exy f3,7=4, f13,7=2, f23,7=3

Q: Sketch the contour map of the function f(x, y) = 4 – Va2 + y? Label the level curves at c= 4, 3, 2,…

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Q: Evaluate . F dr where F(x,y,z) = (cos x, -2x, y + sin(z³)) and C is the boundary of the triangle…

A: This is a problem of surface integral.

Q: Let F(r, y,z) = where r2 + y? < 4, oriented by the upward normal. (r,-z,2y(r2-y²)). Find ff, F- dS…

A: Given Fx,y,z=x,-z,2yx2-y2and S is the saddle surface z=x2-y2, where x2+y2≤4, oriented by the upward…

Q: Find symmetric equations of the normal to the surface, r (u, v) = at a point (1, 1, 3

A: given ru,v=&lt;u2,v2,u+2v&gt; therefore ru=∂∂uu2i+∂∂uv2j+∂∂uu+2vk=2ui+0j+k…

Q: Find an expression for a unit vector normal, no, to the surface x = (4 – cos (v)) cos (u), y = (4 –…

A: The complete solutions are given below

Q: Suppose S is a region in the xy-plane with a boundary oriented counterclockwise. What is the normal…

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Q: Q2) Evaluate ff xy dA Over the region enclosed between y=x, y = vx and x = 2, x = 4

A: Q.2:-Given integral is∫∫xydA region enclosed by y=12x   , y=x   and x=2   and x=4Point of…

Q: Gy Determin thle area between the curve 9 = x²+1 and y+ X = 7

A: Given: To determine the area between the curve y=x2+1 and y+x=7⇒ y=7-x

Q: Solve it using variation of parameters. Less writing , just show the steps of solving

A: Step 1:

Q: Evaluate the line integral by stokes theorem where F(vector)=[ 0, xyz ,0] , C is the boundary of a…

A: Calculate curl:  curlF=ijk∂∂x∂∂y∂∂z0xyz0         =i-xy+kyz

Q: Let F(x, y,z) = (-xe² +3x, -ye² + arctan(x? + z), 2e²) and S the portion of the sphere acoording to…

A: Given that Fx,y,z=-xez+3x, -yez+arctanx2+z2, 2ez. Also, S=x,y,z| x2+y2+z2=1, z≥0. To determine the…

Q: If F(x, y, z) = z - f(x, y) and s is the graph of z = f(x, y) and (a, b,c) is a point on the surface…

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Q: Let f(x, y) = ln (1 + x² + y²), then a) f is not differentiable at (0,0). b) f(xo, yo) = f(xo, yo)…

A: Multivariate calculus

Q: (4) Let S be the part of the plane z = f(x, y) = by (x - 1)² + (y - 3)² ≤ 9 oriented with an upward…

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Q: Give a parameterization for the surface z F(u, v) = (u, v, ). x² - y²: = x

A: NOTE: Refresh your page if you can't see any equations. . the given surface is

Q: Let z = g(x, y) = f(3 cos(xy), y + e=") provided that f(3, 4) = 4, f1(3, 4) = 2, f2(3, 4) = 4. i)…

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