• What is/are the trace(s) of the surface (x – 1)? 22 = 1 on the rz-plane? 36 a. hyperbola b. parabola c. intersecting lines d. none of these а. b. O c. Od.

Q: Consider the rormal line to the surface z= z + y? (parabokoid) at the point P(1,1, 2) Find the point…

A:

Q: Find ervstion for the tangen plare to the Surface an Siven by x2y?3 =12 at the point Z-2,1,3)

A:

Q: (b) Sketch the trace of the surface z = 2x? – y? when x = -1. Label your axes, and give the…

A: Given surface is  z=2x2-y2          (i) By putting x=-1 in (i), the surface becomes z=2-y2 The graph…

Q: The plane y=2 intersects the elliptic paraboloid ē =4x ty parabobo. Fied the slope ot the fangenh to…

A: Given :     y = 2      z = 4x2 + y2

Q: The tangent plane to the graph of the surface z=In(x2+y?) at the point (1,0,0) contains point…

A:

Q: Let C be the curve y 8ī for 1.5 < T < 3.6. %3D 16 15 14 13 12 10 Find the surface area of revolution…

A: the given curve is take derivative

Q: 11. Find the area of the surface obtained by rotating the curve y = a, 0 < a < 3/4, about the a…

A: Surface area of revolution

Q: The area of the surface obtained by rotating the curve y = x2, 0 <x< 12 about the y-axis is

A:

Q: 2. For the surface z = In(y+ Vx² + y²). (a) Find an equation of the tangent plane at the point (3,…

A:

Q: Find the equation of the tangent plane to the surface 2² at the point Y= 2x? (0, –1,2) %3D O y- 2z…

A:

Q: Suppose that an equation for the surface is S(x,y) = xye^x. In what direction (relative to the…

A:

Q: Find the equation of the tangent plane to x² the surface z = + y? 4 - at the point (2, 3, 10) x + 6y…

A: The equation of the tangent plane to a surface f(x,y,z) is given by:

Q: Are there any points on the hyperboloid r2 - y? – 22 = 1 where the tangent plane is parallel to the…

A: Given hyperboloid ;    x2-y2-z2=1  and equation of plne which is parallel to tangent plane  x+y-z=0

Q: te the surface integral /| (32zi + 2zyj+ 2yzk) · ds S is the part of the parabola z = 15 – x² – y…

A:

Q: Find an equation of the tangent plane to the surface z = 2a2 + 1y – la – 3y – 1 at the point (5, 3,…

A: Equation of Tangent Plane to the surface F(x, y, z) = 0 at point (x0, y0, z0) is given by ∇F(x0, y0,…

Q: Determine the projection of the following surface on the xz plane. (xz trace) 4z – + = 0 O Parabola…

A: Solution is given below:

Q: At which of the points below is the tangent plane to the surface z - 2y + z?+ yz = 2 vertical?…

A:

Q: Determine the projection of the surface – y? = z on the yz-plane? (Hint: a = 0) Circle O No answer…

A: The solution is :

Q: Determine the projection of the surface - y = 3. on the yz-plane? (Hint: x = 0) O Parabola O No…

A: Given:      Surface x23-y2=z       By putting x=0 we get             023-y2=z

Q: Consider the surface 4a? – y? + 2z² + 4 = 0. a. Find the value(s) of k such that the cross-section…

A:

Q: Identify a generating curve on the xz-plane for the surface of revolution with equation x2 + y? + 22…

A: Solution :-

Q: The equation of the tangent plane to the surface yey +z =0 at the point (0,-1,1) is az+by+cz = 1.…

A:

Q: For the surface described by z= - 20y+x² – 10x +3y-2xy | a. At what point are both zx=0 and zy=0 %3D…

A:

Q: The area of an ellipse with axes of length 2a and 2b is nab. The percent change in the area when a…

A: Area of ellipse initially  = Ai  = πab    Now, lengths of axis are changed,   They are  [ 2(1.0099)a…

Q: Find the area of the surface that is generated by revolving the portion of the curve y = 2/1-, zE…

A: Use formula of surface area revolved about x axis

Q: Let 13 be the surface with the equation given by 4x²-9y²= 9(z²+4)

A:

Q: For the surface 4x² + y² −z = 0, classify the indicated trace as an ellipse, hyperbola, or parabola.…

A: We have been given the equation  4x² + y² −z = 0           (1)

Q: Determine the projection of the following surface on the plane of the xy-axes -2y? + + =1 3 3 O…

A: -2y2+x23+z23=1To find the projection

Q: Let 13 be the surface with the equation given by 4x²-9y²= 9(z²+ 4)

A:

Q: 9. Show that the sum of the T-, y-, and z- intercepts of any tangent plane to the surface VI + Vỹ +…

A: Given, Gradient of the surface at any point (x0,y0,z0) is given by,

Q: The tangent plane to the graph of the surface z=In(x2+y2) at the point (1,0,0) contains point…

A: Given function is, z=lnx2+y2

Q: Let C be the curve y = 6x³ for 0 ≤ x ≤ 1.3. 13- 12- 11 10- 9- 8- 7- 6- 5- 4 3- 2- 0.5 a Find the…

A:

Q: For the surface a?+ - z = 1, a curve in a form of a parabola can be formed bi passing through a…

A:

Q: Let C be the curve y = 9/ for 1.3 < 3.4. 16 +15 14 12 -구 Find the surface area of revolution about…

A:

Q: At which of the points below is the tangent plane to the surface r2 – 2y? + z2 + yz = 2 vertical?…

A: From the tangent plane to a surface

Q: Find the points on the surface 2a2+ ly? + 522 = 1 at which the tangent plane is parallel to the…

A:

Q: Sketch the curve of intersection of the surfaces. The ellipsoid 2x + 2y² + z? = = 24 and the…

A: We have to write the intersection curve

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: Consider the surface z = 4x2 + y? + 1. An equation for the tangent plane to this surface at the…

A: Let fx,y=z. Differentiate the function f(x,y) partially with respect to x and y, to find fx and fy .…

Q: Determine the projection of the following surface on the xz plane -y+ 름 =1 O Ellipse O Parabola O…

A:

Q: (b) Find the point that makes the tangent plane to the surface z = x- xy +y-2x + 4y horizontal.

A:

Q: The tangent plane to the graph of the surface z=In(x2+y?) at the point (1,0,0) contains point…

A:

Q: Determine the equation of the tangent plane to the surface z=x - 3xy + y at the point P (2, 1, 3).…

A: Solution

Q: B. Let C be the curve y = 1 – x2, 0< x < 1. If C is rotated about the y axis find the area of the…

A: our objective is to calculate the surface area.

Q: The tangent plane to the graph of the surface z=In(x<+y<) at the point (1,0,0) contains point…

A: and point (1,0,0)

Q: Parametrize the intersection of the surfaces using t = z as the parameter. (If there are multiple…

A:

Q: Consider the surface z = 4x2² + y² + 1. An equation for the tangent plane to this surface at the…

A: Given: z=4x2+y2+1

Q: Determine the projection of the following surface on the plane of the xy-axes -2y? + 물 + 물 =1 O…

A: Given data: -2y2+x23+z23=1 ..........................(1) Solution: We have to find projection of…

Q: The tangent plane to the graph of the surface z=In(x2+y²) at the point (1,0,0) contains point…

A: