Draw the parameterized surface. (Decide on a reasonable domain for u and v.)

Q: Draw the Taxi-metric hyperboloid |x| + |y| + |z| = 1

A: As per the question we are given the equation of Taxi-metric hyperboloid as : |x| + |y| + |z| = 1…

Q: 5. Consider the surface: x(u, v) y(u, v) z(u, v) where u € [0, 1] and v € [0,2]. Calculate the area…

A: Introduction: The area is the area occupied by a two-dimensional flat surface. It has a square unit…

Q: Identify and sketch the surfaces y = - (x2 + z2)

A: Given Data The equation of curve surface is y=-(x²+z²)   The sketch of the surface equation is,

Q: determine the type of the quadric surface. ) + G)° + 2:² = 1

A: To determine the type of quadric surface(x3)2+(y4)2+2z2=1

Q: Identify and sketch the surfaces x2 + y2 - z2 = 4

A: Given, The surface is x2 + y2 - z2 = 4

Q: Sketch the surface..........CYLINDERS............. x2 + y2 = 4

A: x2+y2=4 Now, rewrite the above surface for the function as, z=fx,y. z=fx,y=4-x2-y2

Q: (a) Identify and graph the quadric surface -r - y + 2? = 1.

A:

Q: Sketch the surface.......... ASSORTED ............... x2 + z2 = 1

A:

Q: Consider the surface z = (x+ 1)² + (y – 2)² – 1 Does the point (1, 3, 1) belong to this surface?

A:

Q: Draw a figure that shows the image of the triangle with vertices (0, 0), (1, 0), and (1/2, 1) under…

A: It is given that the vertices of the triangle are 0, 0, 1, 0 and 12, 1. We have to sketch the graph…

Q: Use a CAS to plot the implicitly defined level surfaces x2 + z2 = 1

A: The given surface is,

Q: Find the extreme values of ƒ(x, y, z) = x - y + z on the unit sphere x2 + y2 + z2 = 1.

A:

Q: Give a geometric description of the set of points (x, y, z) that lie on the intersection of the…

A:

Q: Determine the location of a point (x, y, z) that satisfies the condition  ∣y∣ ≤ 3

A: If ∣y∣ ≤ 3 the point lies with in 3 units from xz plane on left side if y < 3 , or within 3 units…

Q: 10. Find all the planar and hyperbolic points on the surface o(u, v) = u-3uv².

A: A point on a surface is said to be a hyperbolic point if the Gaussian curvature at p,i.e., κp<0.…

Q: The half-space consisting of the points on and below the xy-plane

A: Concept:

Q: The intersection between the surface x + y + z = - 1 and the circle x2 + y2 = 1,z = 0 is

A:

Q: Give a geometric description of the set of points (x, y, z) that lie on the intersection of the…

A: Given Data The equation of a sphere is x2+y2+z2=5. The value at z-axis is z=1.   Put the values in…

Q: sketch the given surface. x2 − y2 + 9z 2 = 9

A: Given, x2-y2+9z2=9

Q: Sketch the surface z = f(x,y). f(x, y) = -x 2 - y 2 USE GEOGEBRA

A: Function f(x, y) = -x2-y2 To Sketch the surface z=f(x, y).

Q: Sketch and identify the surface given by x2 + 4y + 4z2 = 0.

A: Equation of the surface is given by:x2+4y+4z2=0 we need to identity the surface and hence sketch the…

Q: the normal line of the surface [z = (4x^2 + y^2] at the point (1,1,5) O 8x-2y+z=5 O 8x+2y+z=5…

A: We have to find the normal line of the surface.

Q: Find a parameterization for the quarter sphere x² + y² + z² = a² where z > 0 and x > 0.

A:

Q: sketch the given surface. x = 1 + y 2+ z2

A: sketch the given surface. x = 1 + y 2+ z2

Q: Describe and sketch the surface x2 + z2 = 4

A: Given- x2+z2=4 To sketch- The graph of the above function and explain it.. Concept Used- The…

Q: Find the barycentric coordinates of p with respect to the affinely independent set of points that…

A: Given 11, 35, 06, p=23 let a=11, b=35, c=06, p=23 Now we write the points in augmented matrix form…

Q: consider surtace S with paramtrization. Gcu,v) = cu,V,uv) , tuts of s also compute the surface areu

A: Given that  G(u,v) = <u,v,uv> , u2+v2≤1 Surface area is given by, S=∫∫D|Gu×Gv|du dv To find Gu…

Q: Sketch the surface r = 2y? + 32².

A:

Q: Identify and sketch the surface by plotting different traces of (x – 1)2 – (x + 2)2 - (z + 4)² = 0.

A: According to the given information, it is required to identify and sketch the surface.

Q: Check whether the given surface (x – a)² + (y – b)² + (z – c)? 16 is developable or not. -

A: Given surface(x-a)2+(y-b)2+(z-c)2=16orz=c+16-(x-a)2-(y-b)2If the surface is developable…

Q: 1. Let a, b, c ER and let Sa,b,c = {(x, y, z): ax2 + by2 + cz²=0, x² + y² +2²=1}- (1a) For which…

A: Given: Sabc=(x,y,z): ax2+by2+cz2=0, x2+y2+z2=1 To find: the values a, b, c for which Sabc a regular…

Q: Identify and sketch the surfaces z = - (x2 + y2)

A: Identify and sketch the surfaces z = - (x2 + y2)

Q: The portion of the surface z = 2x + y2 that is above the triangular region with vertices (0, 0), (0,…

A:

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

A: To sketch the function

Q: Surface o is a plane a +y + z = 1 that lies in the first octant. Evaluate

A: Given, surface σ is a plane x+y+z=1 that lies in the first octant. To find              ∬σ(2x+z)dS=…

Q: Evaluate ∬S(x2+y2)dS, where S is the surface z=4−x, 0≤x≤2, 0≤y≤2.

A: Given z=4-x , 0≤x≤2 ,0≤y≤2 to evaluate ∬Sx2+y2dS where S is surface

Q: Describe the usual orientation of a closed surface such as a sphere.

A:

Q: Exercise 3. Prove that M = {(x, y, z) | (x² + y³)² + z² = 1} is a surface. (Hint: this surface is…

A:

Q: Evaluate [[[ =*dxcydz over the sphere x +y² +=² =1.

A: to find:- to evaluate the given integral.

Q: Consider the surface S given by: S :r(u, v) = (uv², u + v, v³), u E [0, 1], v E [0, 2]

A:

Q: The quadric surface 2 = x² + is called

A: We know that this is the equation of hyperboloid from the general equation of hyperboloid.

Q: (a) Find max, min or saddle points for the surface Z= x* - 3xy + 5x

A: We have to find first and second order partial derivatives.

Q: Classify and Sketch the surface X2+ Zy² + Z? -4x+4y-2z+3:0

A: The given equation of the surface is x2 + 2y2 + z2 - 4x + 4y - 2z + 3 = 0.The general equation,…

Q: Determine whether the points P and Q lie on the given surface. r(u, v) = (3u + 2v, 2 + 5u – v, 4 + u…

A:

Q: 9. f(z) = e'n/4z %3D

A:

Q: What is the surface of the box formed by the net above

A:

Q: EXERCISE 3.2 A parametric surface is P(u, w) = [0.5(1 − u)w + u, w, (1 − u)(1 − w)]. 0 ≤u, w ≤ 1.…

A: We have  parametric surface is P(u, w) = [0.5(1-u)w+u, w, (1-u)(1 − w)]. 0≤u, w≤ 1.   We have to…

Q: Let y ==a and z =. Find the intersection of these х x2 surfaces.

A:

Q: Sketch the surfaces ASSORTED x2 + y2 = z

A: we have to sketch the surface x2 + y2 = z.

Q: Describe and sketch the surface y = z2

A: Solution: Consider the given surface y = z2 On the y z-plane, it represents a parabola that opens in…

Q: 7. Sketch the surface 1≤z≤2-x² - y²

A: