Find an equation for the surface obtained by rotating the curve y = √ √x about the x-axis.

Q: Find the slope of the tangent in the positive x-direction to the surface z = 3x - 6xy at the point…

A: We have to find the partial derivative with respect to x

Q: Find the distance between the point (p, 4p) and the parabola y? = 2px, where p is a fixed positive…

A: let the point on parabola be A= (x, y)  B = (p, 4p) Thus,  AB = x-p2+y-4p2 but parabola is y2=2px…

Q: III. Consider the parabola C: z-4 = -(x - 2)² on the xz-plane. 3. Give an equation for the surface…

A: Given equation of parabola is:.The objective is to find an equation of the surface of revolution…

Q: Find the equation of the surface of revolution that is generated by rotating the straight line y = x…

A: The surface of revolution that is generated by rotating x=f(y) around the y-axis is x2+z2=f(y)2 so…

Q: Find an equation of the surface of revolution obtained by revolving the plane curve 4x² – y² = 4…

A: The given equation of plane curve is 4x2-y2=4. Since the plane curve is rotated about x-axis,…

Q: Explain what it means for a surface to be orientable.

A: They are the surfaces for which we can define clockwise consistently. e.g. Cylinder and spheres are…

Q: The equation z = f(x,y) = y +x -3y defines a surface. What is t- equation of the tangent plane at…

A:

Q: I need a 3d sketch of the equation  Z=x+xsiny+xy

A: z=x+xsiny+xy

Q: Find the equation for the tangent plane to the surface z = - 9x - 7y at the point (2, 1, - 43). O A.…

A:

Q: Find an equation for the surface obtained by rotating the line z = 7y about the z-axis.

A: On solving this we will get

Q: Find an equation of the tangent plane to the surface at the given point. x²+²-72²-38, (-3, -6, 1)

A:

Q: Find an equation of the tangent plane to the surface z = 2y² – 3x² at the point (-3, -3, -9).

A:

Q: Find the equation of the tangent plane to the surface z = 6x4 + 5y + 3xy at the point (-3,0, 486). z…

A:

Q: (a) x² + 2x + 4y² + 16y + 9z? 19

A: Sketch and identify the surfaces: (a) x2+2x+4y2+16y+9z2=19.

Q: dish whose shape will be formed by A group of engineers is building a parabolic sa rotating the…

A: Formula: The surface area obtained by rotating the curve y=f(x), a≤x≤b,  about the y−axis is given…

Q: The following equation is an equation of a surface of revolution obtained by rotating a curve C…

A: The given equation of surface of revolution is x2+y2+z2=1. This equation can be written as:…

Q: Q3. Find the point(s) on the surface xyz 1 closest to the origin. %3D

A: Given: To find the points on the surface xyz=1 is given as,

Q: Find an equation of the tangent plane to the surface at the given point. z = x2 + y? + 6, (1, 3, 16)

A: