A 2-D surface was found in one research group of scientists and a surface equation has been derived as f(x, y) =x* + y* –16xy. a. Find f,,S,,SSy b. Find the stationary points and determine the types of each stationary points. (Hint: Hessian of ƒ is H =144x²y² – 256)

Q: x² T +3y² = z + 3. Consider the surface T with equation 3 1. Find the equation for the trace of T on…

A: Solution

Q: 2. Find the distance between the line with parametric equations ï = 1 + 2t, y = −2+ 4t, z = 4 − 4t…

A:

Q: 7. A curve in the zy-plane is described by the equation 2y(x − 1)² – xy² + 1 = 0. (a) Determine…

A: Given equation of curve: 2yx-132-xy2+1=0 Now, from the given points (1,0) , (2,0), (1,1) , (2,1) and…

Q: = (9,4, 5) w = (10, 10, 10) Find the cosine of the angle between v and w. cos 0 =

A:

Q: Find the equation of the tangent plane to the surface z=e-4x/17ln(1y) at the point (-3, 4, 2.808).…

A: The given function is z=e-4x17lny and the given point is P-3,4,2.808. We know that the tangent plane…

Q: 4. First, sketch a picture of the line which passes through P = (1, 1, 2) that is perpendicular to…

A:

Q: Determine the surface area of the plane 2x+y + 2z = 16 cut off by x = 0, y = 0 and x² + y² = 64.

A: Area of surface given by z = f(x,y) A=∫∫Dfx2+fy2+1dA  where (x,y) is a point from the region D in…

Q: 2. XY has an endpoint X at (2,– 4). If the midpoint of XY is (– 3,– 1), what are the coordinates of…

A: The midpoint of two points and is given by: where are coordinates of the midpoint.

Q: 5. Find u-dr for a unit square in the first quadrant with vertex at the origin by Stokes's C theorem…

A:

Q: 21. Let Sech u = 3/5 , determine the values of the remaining five hyperbolic functions.

A:

Q: 4x2 + 2. Let S be the surface with equation y = 9 (a) Write the equation of the traces of S on the…

A:

Q: 4x2 + 22. Let S be the surface with equation y = (a) Write the equation of the traces of S on the…

A:

Q: III. Let S be the quadric with equation 4x² − (y - 3)² + 4z² = 4. a. What type of quadric is S? Find…

A: Here we are given a 3d surface S by the following equation : 4x2 - (y-3)2 + 4z2 = 4 And we have to…

Q: Sketch a contour map and graph of . a. g(x, y) = 9x² + 4y² b. z = y/x

A: The given function is: g(x, y) = 9x2 + 4y2 The contour map of the above function is:

Q: 3. Explain what is wrong with the following statement: If R,T are corresponding regions in the xy…

A:

Q: 1. Find all points on the graph of h(x, y) = plane is horizontal. 3x²9x + 4 + 2y³ - 12y where the…

A:

Q: Which of the following point (æ, y) on the graph of y = /2x is the nearest to the point (4,0) ?…

A: 1. The parametric form of equation Y2= 4aX is X = at2 and Y= 2at. 2. The perpendicular distance from…

Q: 3. The point D is the centroid of AABC. Find the value of the distance DC if : GD = 2x – 8 and GC =…

A: It is known that the centroid of a triangle is the point at which the 3 medians of the triangle…

Q: Зу — 2z 3D 6

A: Use a graphing utility to plot the plane, 3y-2z=6 .

Q: 4. Find the values of x and y as shown below if three lines are parallel. (5y-4) 3y (2x+13)

A: