Graph the solid that lies between the surface z= 2xy/( x2 + 1) and the plane z =x + 2y and is bounded by the planes x =0 x= 2 y = 0 and y=4 x=-1, y =0 and y =4

Q: Find a point on the surface x+4y--z² =1 where the tangent plane is parallel to the plane x+4y- z =…

A: we need to find gradient of given surface to know about direction of normal vector to tangent plane

Q: For a given surface z-x^2-y^2=10 Find the parametric representation of the straight line which…

A:

Q: Sketch or describe the surfaces in R³ of the equation presented x² + y} – 2x = 0

A: The equation is x2+y2-2x=0

Q: - Graph the surface 1 = y² + z² — by first sketching at least three cross sections in each of the xy…

A: To Plot: Graph The Surface 1=y2+z2-x24 by plotting at least three cross section in xy and yz plane

Q: Find the slope of the tangent line to the curve of the intersection of the surface x² + y² +2²= 9…

A: The tangent is the line that just touches the curve at a single point. In this problem, the curve is…

Q: 3. Find the area of the part of the surface x 2z + y° - 3, that lies above the triangle in the…

A: Given, x=2z+y2-3, i.e. z=12x-y2+3. As it is known that the surface area is given as,…

Q: /Sketch the Surface Z=V9-X+y- and verify that fxg = Exx %31

A: Second order Partial Differentiation

Q: Describe and sketch the following surfaces z = f(x, y): (a) * (c) 2= /1-x² - y² z = 6 - 2x - 3y (b)…

A: We have to sketch and describe the following curve

Q: Give equations for two distinct planes whose trace in the yz-plane has equation y = 4z

A: Given, two distinct planes have trace in the yz-plane has equation y = 4z

Q: Find the distance between the point (0,0, 8) and the plane given by 2x – y + 2z – 1 = 0.

A:

Q: Sketch the surface given by the equation x2+z2/3+y=3 indicating the points where the surface…

A: Sketch the surface given by the equation x2+z2/3+y=3   indicating the points where the   surface…

Q: Consider the curve r(t) = (a) Pick any three points along the curve. Then find an equation of the…

A:

Q: Describe the surface whose equation is given by x² + y² + z² + 6y - 2z = 0.

A:

Q: Sketch the surface of f(x,y)

A: To sketch the function

Q: Suppose you head toward the xy-plane from the surface x? + y? – 2² = –1 at the point (1, 1, v3) by…

A: given,     x2+y2-z2=-1 at the point 1,1,3

Q: Find a parametrization of the curve of intersection of the surfaces z = x² – y² and z = x² + xy + 1.

A: The given curves are z=x2-y2 and z=x2+xy+1 To find the intersecting curve : Let us equate both the…