Parametrize the intersection curve between the graph z = x² + y² og plane x - y = 2. Find the equation of the tangent plane to the graph z = x² + y² at the point (-1,2,5) on the graph Find the volume of the body that lies above the xy plane and below the graph of the function f(x,y) = 25 - x² - y²

Q: find the angles between the curves v=u2, v=u3, lying on the surface  x=u2+v2 y=u2-v2 z=uv+3u+2v

A: As per the question we are given the parametric form of a surface in 3d as : x = u2 +v2 y = u2 - v2…

Q: Find an equation of the line tangent to the intersection of the cylinders x² + z² = 4, y² + z² = 4…

A: The parametric form of the tangent line is  x=x0+aty=y0+btz=z0+ct where, (a,b,c) is the direction…

Q: In how many ways can one put 8 adults and 4 children in a row, such that no two children are next to…

A: We have given that there are 8 adults and 4 children in a row. Here our claim to to show in how many…

Q: obtain the gradient of the function f(x,y,z)=x^2y+5xz

A:

Q: et C be the curve of the intersection of the two surfaces a² +} = z and 4x2 +y} +? =9. nd let L be…

A:

Q: Find the tangent planes to the surfaces given by the equations z = 7x^2 - 12x - 5y^2 and xyz^2 = 2…

A: NOTE: Refresh your page if you can't see any equations. . the first surface is so we can write…

Q: Prove by induction on n that for all positive integers n, n3 + (n + 1)3 + (n + 2)3 is a multiple of…

A: The given statement is n3+n+13+n+23 is a multiple of 9 for all positive integers. We have to prove…

Q: For f(x, y, z) = x^2 − 6x + y^2 + z^2 , describe and draw the level surface for the function value…

A: Let w=f(x,y,z) . The level surfaces of w=f(x,y,z) results, when w=k slices the the function,…

Q: A thin metal plate of uniform density covers the area between the curves y = 2+ 6x – x² and y = 2 –…

A:

Q: Use partial derivatives to find the coordinates which give the shortest distance from the point…

A:

Q: Find equations of the tangent plane and normal line to the surface x = 5y² + 5z² — 28 at the point…

A:

Q: Find a point on the surface z = 3x^2 − y^2 at which the tangent plane to this surface is parallel to…

A: We need to find the Point on the surface of  z=3x2−y2 given tangent plane to this surface is…

Q: Tangent to the surface, find an equation of the

A: Introduction: The formula of the tangent plane from the equation fx,y=z at the point a,b,c is given…

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.

A:

Q: Weight of whales:  The equation W= 3.51L -192, expressing the relationship between the length L (in…

A: The given equation is W = 3.51L -192. The above equation expresses the relationship between the…