1. In R2, what is the dual cone V* if the primal cone V is V = {y1 (-3, -4) + y2 (1, -3) | y >= 0}

Q: Let P denote the path that travels along the graph of y = x2 from (0,0) to (1,1). Let f(x,y) = √1 +…

A: Let P denote the path that travels along with the graph of y=x2 from (0, 0) to (1, 1). Let f(x,…

Q: 42. Show that the graph of d ae""cos wi is bounded by y = ae-ct and y = -ae-ct for a > 0 and c> 0.

A: We know that,

Q: 6. Consider the PDE u; +u ux - u Uy = 0 for - ∞<x< ∞, - ∞<y< ∞, and 0 <t< ∞ with u (0, x, y) = (x -…

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Q: Find the first piece S1 (x) of a natural cubic spline that interpolates the set of points (0,1),…

A: Formula for cubic spline interpolation is…

Q: Chapter 15, Section 15.1, Question 018 Find div F and curl F. F (x, y, z) = xz" i + 6y"x² j+ 3z²yk…

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Q: b) Is there a linear map T: V → W, where dim V = 3, dim W = 4, rank T = 2, and dim ker T = 1?

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Q: 5. Prove that the baker map 2x B(z) = 2z - 1 <z<1 is chaotic on (0,1).

A: Given the baker map, Bx=2x,0≤x≤122x-1,12≤x≤1

Q: If F(x, y, z) = (x²z, –2xz, yz), then curl F(6, –3, 1) equals %3D O (12, 39, –5) O (9,34, 2) O (13,…

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Q: 1. E is a triangle with vertices (1,0,0), (0, 3,0) and (0, 0, 2), with 8(x, y, z)=xz+1.

A: Note: As per our guidelines we are supposed to answer only one question and the rest can be…

Q: Compute I ds over the path C : ř(t) = (t², 2t, t²) from (0,0,0) to (4, 4, 4).

A: Given path is:

Q: Consider thế iñifial a. 2y"- 30y" + 150y' – 234y = 0, b. y"+ 6ay' + (9a² + 1)y = 0, y(0) = -3, y(0)…

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Q: Let, T:R' → R³;T(x,y,z)=(2x+ y, y- z,2y+4z) 2. Find the rank and nullity of T.

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Q: 4. Evaluate . F.ds , where C is the triangle with vertices (1,0,0), (0,2,0), and (0,0,3) oriented by…

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Q: Given that vec F =x^ 2 y hat i -(z^ 3 -3x) hat j +4y^ 2 hat k find the k- component of ( nabla* vec…

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Q: Show that the integral S. (3x²y + y)dx + (x3 + x)dy is independent of path, if it is, then evaluate…

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Q: (6) I. adv, where E is bounded by the planes z=0, y = 0, =0, y+= =1 and +=1, as shown in the figure…

A: Given that,

Q: dz Let z-ay" – 4r, * = uv and y-v - 3u. Compute Ən (u,r)-(1,1) -

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Q: 5. Show that the compatibility condition for the Neumann problem V²u = f in D du on B an is f dS +,…

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Q: 12) Find the clamped cubic spline for the data (1,1),(3,4), using that f'(1) = 2, f'(3) = 5

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Q: Compute I ds over the path C : ř(t) = (t², 2t, t²) from (0, 0,0) to (1, 4, 4).

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Q: Find the bounded solution of au Əx = 2 อน at + U_if_U(x, 0) = 6e-³x. 1

A: Given: The equation is ∂u∂x=2∂u∂t+u and the given initial condition is ux,0=6e-3x. To find: The…

Q: 1)Prove that the curves o, = {|z|=2} y 0, = {|z- i|=4} are homotypic. 2)calculate O z*dz and o z*dz…

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Q: 2) Determine the dimension of Null A and Col A for the marix [1 2 3 0 0 A =|0 0 1 0 1 0 0 0 1 0

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Q: 2. Solve the following Cauchy problem: xyu, + yu, + yu = y – x with 1 u = -- y = x². on

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Q: 3 4 Let y = -7 and u = -6 -4 1 Compute the distance d from y to the line through u and the origin. d…

A: The projection of a vector on a plane is its orthogonal projection on that plane. In simple words,…

Q: If the function f is defined on the disk x2 + y² < 1, then f has a critical point somewhere on this…

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Q: 0, 2 is defined by A natural cubic spline S on 5. So()12x - 0 if 1 (1) S(r)2b(x1)c(x - 1)2d(x - 1)…

A: 5.Note that, the natural cubic spline must satisfy the conditions

Q: xy−5yz−7xz,x=st,y=e^(st),z=t^2 Compute ∂w/∂s(1,−2)=

A: The equation given as  w=-2xy-5yz-7xz , x=st , y=est ,z=t2. The partial derivative of the function…

Q: 1. 2. The area bounded by y = = -(x - 1)² + 4 , and the lines x =1, y = 2, and y = 4 rotated about…

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Q: 4 6 Let y = 7 2 40 Compute the distance d from y to the plane in IR spanned by ui and uz d =

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Q: 1. In R2, what is the dual cone V* if the primal cone V is V %3D {y1 (-3, -4) + у2 (1, -3) |у »3 0}

A: Given: V={y1(-3,4)+y2(1,-3)|y&gt;=0}

Q: 1- If z = 1+ y2, we can write: a) z = 1- (iy)?, b) z = 1- iy?, c) z = 1- iy, d) z 1 + (iy)? 2- If z,…

A: As you have posted multiple questions so according to our guidelines, I answered first three…

Q: 1. Sketch the path C which is around the paths one from z = 3i to z = 2i and another from z = 2i to…

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Q: Let a and b be nonzero and f(x, y) = (ax + by)e-x Show that if a ± b, then there are five critical…

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Q: 4 Let y = U2 = -7 U1 = -4 4 -6 -2 -9 Compute the distance d from y to the plane in IR° spanned by u̟…

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Q: Which of the following is a nonlinear second order nonhomogenous PDE a. xux-Uxx=tuxt O b.…

A: To find - Which of the following is a nonlinear second order non-homogenous PDE x ux - uxx = t uxt…

Q: -6 3 Let y = -5 and u = -4 -2 Compute the distance d from 3y to the line through u and the origin.

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Q: 32. Let y = (1, 2, 6) and u = (1, 1, 1). Compute the distance from y to the line through u and the…

A: line through u(1, 1, 1) and v(0, 0,…

Q: 5. Find the curl of U = e*yax + sin(xy) a, + cos² (xz) az. A. 2z cos(xz) sin(xz) a, + [x cos(xy) –…

A: FORMULA USED- For  f¯=pax+qay+razcurl f=axayaz∂∂x∂∂y∂∂zpqr

Q: graph the points z = x + iy that satisfy the givenconditions. | z |&gt; 2

A: Complex numbers

Q: 13 ABCD is a trapecium with ABDC. A line parallel to AC intersects AB at X at Y Prove that ar…

A: Since you have asked multiple question, As per our policy we will solve the first question for you.…

Q: 5. If 4=2xy į +3x°y -3pyzk is solenoidal at(1,1.1). Find p.

A: DivA=0

Q: 4) Let f(r, y, z) = In(r + 2y + 3z). Find Vf = . %3D

A: Given: f(x, y, z)=ln (x+2y+3z)

Q: 2. Solve the following Cauchy problem: u, + 2ru, - u=a+3ye" with u= 2r - 1 on y=-

A: We have to solve the given Cauchy problem.

Q: What is the additional condition for a cubic-spline S(x) that passes through n data points (x1, Y1),…

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Q: In C[0, 27], with the inner product -2 (f, 8) = | f(x)g(x) dx, show that the set S = {1, sin x, cos…

A: Given: Inner product defined as: &lt;f,g&gt; = ∫02πf(x)g(x)dx To show that the set S = { 1, sinx,…

Domain

In simple mathematics terms, a domain is defined as the space on which all the possible inputs for the function will lie. It can also be expressed as a set of departures for the required function.