(a) Integrate g(x,y,z) = lnx'+y over the surface of the region cut from the plane 4x+3y+2z=1 by the cylinder whose walls are x+y=8 and x²-y=0. FA

Q: Show that the curve r= Vti + Vtj + (2t – 1)k is tangent to the surface x +y² – z = 1 when t=1

A: Given that r=ti+tj+2t-1k and f=x2+y2-z-1 Take the derivative for f, ∇f=ddx,ddy,ddzf=2x,2y,-1…

Q: Find the sum of maximum and minimum values of the function f(x, y, z) = 3x+6y +9z 18 and the plane…

A: Now,

Q: 3. (a) Show that the two surfaces S1 : z = xy and S2 : z =3x^2/4 - y^2 perpendicularly at the point…

A: As per our guideline, we are supposed to solve only first subpart. Kindly repost other subpart as…

Q: At what point on the ellipsoid x² + y² + 9z² = 1 is the tangent plane parallel to the plane x + 2y +…

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Q: Let f(x,y)=−5x^2−5y^2+3/2x. Let R be the region bounded by the curve x=25−y^2−−−−−−√ and the y-axis.…

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Q: 10. The part of the paraboloid x = y² + z² that lies inside the cylinder y² + z² = 9

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Q: Cite 1 example of real-life application of midline theorem.

A: Midline theorem:  In the triangle, the line segment that joins the midpoints of two sides of a…

Q: Given F(x,y,z) = (xz-y, yz+x, z^2) (F: R^3->R^3) How do I find the flux of F through the sphere x^2…

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Q: Let p and q represent the following statements. p: You studied. q: You passed this course. Enter…

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Q: What are the coordinates of X' for the image of ATUX after dilation with center at (0, 0) and scale…

A: The coordinates of given triangle are T-7,-6, U-8,3, X2,1. To Find: New coordinates of X if the…

Q: the voulme of the region are  bounded by the paraboloid x= y^2+z^2 and the half cone x=…

A: The volume of the region bounded by the paraboloid x= y2+z2 and the half cone x= 8y2+z2

Q: Let S be the passage of R ^ 2 defined by the parabola with equation y = 18-x ^ 2 and by the line…

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Q: A) Integrate f(x, y) = xy^2 over the square bounded with endpoints at (0, 0), (0, 1), (1, 0) and (1,…

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Q: Calculate the total effect of the wind  (W(x,y))  = ) along the path which is out the line  Y = 9x…

A: Given the vector field wx,y=ycosxy,xcosxy. Consider the path y=9x, x∈0,3. Let us parametrize the…

Q: The path C is a line segment of length 13 in the plane starting at (2, 2). For f(x, y) = 5x + 12y,…

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Q: Find the local linear approximation to f(x, y) = 4x² + y² at P(2,3)

A: We have to find the linear approximation of above function at (2,3) please see the explanation…

Q: Find the Largest open rectangle in the plane in which the hypotheses of Existence and uniqueness…

A: Answer

Q: If the circles x\power{2}+y\power{2}+2a'x+2b'y+c'=0 and 2x\power{2}+2y\power{2}+2ax+2ay+c=0…

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Q: 2.- Let R be the region of the xy plane bounded by the graphs y = x^2; y = 2x, evaluate: L(x³ +4y)…

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Q: The roof of the Monterrey Campus gymnasium has the shape of the hyperbolic paraboloid given by the…

A: Here we have to use directional derivative  Directional derivative of a function f(x,y,z) in the…

Q: Find the absolute minimum and absolute maximum values of the function f(x,y)=x^4+y^4-4xy+4 on the…

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Q: Find the extreme values of the function f(x, y, z) = xy + z^2 on the circle in which the plane y - x…

A: Given function is fx,y,z=xy+z2. We have to find the extreme values of the given function on the…

Q: Let f(x, y, z) = x^2 - y^2 – z. Describe the level surfaces.

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Q: Integrate f(x, y) = 2x over curve C given that C is the part of y = 2x^2 from (2, 8) to (

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Q: Find the parametrization of the curve defined by the intersection of the two surfaces y = x^2 − 3z^2…

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