Parametrize the following. Don't forget to include the limits for your parameter(s). (I'm asking you to find parameterizations for the following curves and/or surfaces). (a) The curve which is the intersection of the cylinder x+y = 4 and the surface x=4+=+2y*. (b) The surface which is the part of the cylinder x +y =9 between the planes = = 1 and =10. (c) The surface which is the part of the sphere of radius 4 which is "behind" the plane x = 0 (that is, the part the sphere of radius 4 in the octants where x <0) and is above the cone =4x+4y.

Q: please solve

A:

Q: Describe and graph (using a computer) the surfaces d) 4y² + z² − x − 16y - 4z + 20 = 0 e) x² - y² +…

A: The given surfaces are: d  4y2+z2-x-16y-4z+20=0e x2-y2+z2-2x+2y+4z+2=0f  fx,y=1x-y2 We have to…

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: Identify the type of quadric surface defined by the equation and find all x-, y-, and z-intercepts…

A:

Q: Match each parametrization with the corresponding surface. (i) (ii) (iii) (iv) (v) Answer Bank (u,…

A:

Q: y -0.5 -0.75 1.5 0.5 0.25 -15 |(1) (2) (3) |-1.75 1.5 -0.5 0.5 0.25 -0.5 y y -0.5- 0.5 -이125- 0.5 -1…

A: Matched surfaces and contour diagrams:   Surface              Contour diagram (a)…

Q: Find the center and radius of the sphere given by the equation x^2 + y^2 + z^2 + 4x − 6z + 4 = 0.…

A: Given equation of a sphere x2+y2+z2+4x−6z+4=0

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: (4) Sketch the surfaces. Show some work including intercepts. (a) z² + 2? = 4 (d) + y² + z² = 1 (b)…

A: Since you have asked multiple questions, we will solve the first question for you. If you want any…

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

A:

Q: 2. -) Consider the surface x² + y²-2xy-x+3y-z=-4 at the point Po(2, -3, 18). Determine the…

A: Let's find equation of tangent plane and parametric equations of normal line.

Q: Consider the function f(x, y, z) = 3x² + y² - 4z. i) A contour surface S passes through the point A…

A: To find the value of the contour surface passing through the point A = (2, 3, -1), we need to…

Q: 4. Find an equation of the tangent plane to the surface z = xy+8 xy-2x at the point (1,1,–10)

A:

Q: 1. Find the elements of surface area dS and dS, in terms of du and dv, for the surface S given…

A: Vector calculus

Q: e'y x+y² a) Find the equation of the tangent plane to the surface at the point P(0, -2). Present…

A:

Q: 16. Use the transformation x = u – v², y = 2uv to evaluate the integral r2Vī-x Vx² + y² dy dx.…

A: