(2) (a) Is the triangulated space ABD, BCD,CED, ABF, BCF, AEF, ADF, AED on a surface? (b) Let y be a graph with 105 many non-equivalent minimal cycles. Find x(7).

Q: Consider projection operator, if x() is global minimum, is x(+¹) = II[x(k)] = x(k) ? True False

A: Given x(k) is global minimum is xk+1=∏x(k)=x(k)

Q: 2 1. Given a space curve a:1= [0,2m] → R³, such that a ()= a(), then a(t) is... Curve A. a closed D.…

A: Solution : 1  Option ( B) is correct  Simple

Q: The graph of f(x,y)=y2-x2 on XYZ space has a saddle point (a,b) if... Choices: A) D(a,b)=0 B)…

A:

Q: #2. Consider the function f (x,y) = x +y-xy on the set D which is the closed triangular region with…

A:

Q: Let G = Z4 x Zp, and S = {(1,0), (3,0), (2,1), (0,1). Prove that Cay(G, S) is not normal Cayley…

A: To prove cay(G , S) is  a normal Cayley graph you need to prove that for any a∈G a-1Sa=S ∀a∈Z4×Z2=G…

Q: Suppose X is a topological space, Y is a Hausdorff space, and f: X → Y is continuous. Show that the…

A:

Q: Find f -6xydA over the triangular region D with vertices (0,0) (2,0), (0, 4) O68 -68 )-8 -16 16

A: Consider the integral

Q: Let f(x, y)=/2x² +4y² + 18 – x. The domain of c for which the level curve f(x, y)=c is an ellipse is…

A: Given fx,y=2x2+4y2+18-x. We need to find the values of c for which the level curve fx,y=c is an…

Q: Prove that the system of parabola y2= 4a(x+a) is self orthogonal

A:

Q: Let f(x, y)=V2x2+4y2+8-x. The domain of c for which the level curve f(x, y)=c is an ellipse is O…

A: Equation of ellipse : (x-h)2a2+(y-k)2b2=1 Where (h,k) is coordinate of centre of ellipse

Q: 1. Find the absolute maximum and minimum values of the function 2u2) on the set D where D is the…

A: We have been given the function f(x,y)=e-x2-y2(x2+2y2)      (1) on a set D x2+y2≤4 where D is the…

Q: Problem 4: The parts (a) and (b) of this problem are independent of each other. G1 G2 6 (a) Prove…

A: we are given two graphs G1 and G2

Q: QUESTION 3 Calculate OF.dr if F= and C is the triangle oriented counterclockwise with vertices at…

A: please see the next step for solution

Q: S :R\{0} → R, S(r)=e4z^+5z=2–1

A:

Q: Find the maximum and minimum points of the surface x2 - (y – 6)² + 2z² = 16 on the sphere x2 + y2 +…

A: Given a surface : x2-(y-6)2+2z2=16  We need to find maximum and minimum points of the given surface…

Q: 8. (a) Show that the system i=y+xf(r)/r, j=-x+yf(r)/r (7=x²+y?) (*) has limit cycles corresponding…

A: Given part (a) x·=y+xfrry·=−x+yfrrr2=x2+y2 By transforming coordinates into polar coordinates Thus…

Q: Let p(x) = kx* + kx + kx + k,x + kg, x E R be a polynomium without a first degree term whose graph…

A: The given polynomial is: p(x)=k4x4+k3x3+k2x2+k1x+k0

Q: nd the orthogonal trajectories of the family of confocal central conics given as: = 1 a² + à b² + à

A:

Q: Consider the following. 3x + 3y + 7z = 63 Sketch a graph of the plane. 10 10 10 10 20 10 10 20 20 20…

A: Given equation of plane is 3x+3y+7z=63  ---(1)

Q: Each nonempty can be represented as the convex hull of its extreme points. --------

A: Each of the nonempty compact convex set can be represented as the convex hull of its extreme point.

Q: Let f(x, y) =V 2x² +4y² +8 - x. The domain of c for which the level curve f(x, y) = c is an ellipse…

A: We have to solve given problem:

Q: -}]-=[}]»=[}- [] 3 Find Let vị = and p = 3 a hyperplane [f: d] (in this case, a line) that strictly…

A:

Q: Question 6: How many different paths in the xyz-space are there from (0,0,0) to (3,4,5) if a path…

A: We have to find the number of paths in the xyz-space from (0.0.0) to (3.4.5) if a path proceeds one…

Q: Consider projection operator, if à() is global minimum, is ä(k+¹) = II[x(k)] = x(k) ? True False

A: X(k) is global minimum if     f(x(k)) <= f ( x)    for all x in Rn  This implies  If we take x =…

Q: attern on the graph as well as the space provided

A:

Q: In Exercises 1-12, sketch the graph described by the following cylin- drical coordinates in…

A: Since we are given with the multiple number of question and our guideline is solve first question…

Q: 5. Evaluate 2XZds where S is the part of the plane - 2x +4+Z =3 over the triangle with bounds…

A:

Q: Prove that the curves o_1={|z| =2} and o_2= {|z-i|=5} are homotopic.

A:

Q: Prove non-existence of limit cycles for the system i = y? – x, ý = -y + 2xy + 2y by a) using index…

A: PART A The given system is : x˙=y2-xy˙=-y3+2xy+2y Now, the equations will be , x˙=0y2-x=0x=y2 Also…

Q: 6.8. Show that the conic hull of the set S= {(xj,x2) : (x, – 1) +x} = 1} | is the set {(x1,x2) : x¡…

A: Given S=x1,x2:x1-12+x22=1 We know that conic hull of a set S is the set ∑i=1nxiαi: xi∈S, αi≥0, n∈N…

Q: Problem 4. Prove that a continuous surjection from a compact space to a Hausdorff space is a…

A:

Q: 1. Let F(x) = x. Compute the first five points on the orbit of 1/2.

A: Given:    F(x) = x2   First five points on the orbit of (1/2)

Q: Find the vertex of the paraboloid z=x2+4y2−xy+6x−5y+1

A: The paraboloid is of two type, one is elliptic and another is hyperbolic ,  By suitable choice of…

Q: caculate and generate the graph of following general cylinders and surfaces in three dimensions.…

A: Given equations are  1. 9x^2 + 4y^2 =36 2. z=16-x^2 3. 9x^2 + 4y^2 +z^2 =36 4. 9x^2 + 9z^2 - 4y^2…

Q: , a curve in the z-plane and a complex mapping w = f(z) are given. In each case, find the image…

A:

Q: Let f(x, y)=V2x2+4y2+8-x. The domain of c for which the level curve f(x, y)= c is an ellipse is 0…

A:

Q: Let f(x, y)=V2x²+4y+32-X. The domain of C for which the level curve f(x, y)= C is an ellipse is O…

A:

Q: Consider the following subsets of real plane R termine with graph: Arcwise connected A = ((x,y): 0 ≤…

A:

Q: 1. Consider the system ' = 3x + 6xy?, W =x² + 1. Are there any closed orbits? Explain your answer.

A: Given - Consider the system  x' = 3x + 6xy2, y' = x2 + 1. To find - Are there any closed orbits ?…

Q: Suppose that G is a graph such that uvory subgraph H of G contains a vortex of degree at most k…

A:

Q: Let y = Vxy, y(xo) = yo- %3D %3D Find all points (x0, yo) in the xy-plane where an existence and…

A: Given that  Y'= √xy Y(Xo) =Yo

Q: Suppose a surface in three-dimensional space has the equation ax^2+bx+cy^2+dy=z  and it contains the…

A: A given set of points can be assumed to be on a surface given by an equation when the each of…

Q: Let f(x, y)=V2x+4y² + 18-x. The domain of c for which the level curve f(x, y)=c is an ellipse is O…

A: Given function, fx,y=2x2+4y2+18-x To find the domain.

Q: Show that the “conic” x2 + 3y2 − 6x + 12y + 23 = 0 has no points.

A:

Q: The graph of f(x,y)=y2-x2 on XYZ space has a saddle point (a,b) if... choice: (choose one correct…

A: Objective is to find the condition for saddle point

Q: 4. Show that the distance between the two points z1 and z2 in an Argand diagram is |z1 – z2). In…

A: (6) z-1=2 Given that:The points z=x+iy satisfies the condition z-1=2 The complex number z=x+iy…