3. Use Green's Theorem to evaluate G³ï+xj)•dr around the perimeter of the rectangle 0

Q: 4. Consider the point M 2t,31 – 1,-t+ Determine t for that M belongs to the mediator plane of [AD].

A: Question: (4) Given points A-1,4,2,B1,1,0,C-3,5,-32 and D232,15,10 Objective is to find the value of…

Q: Use Green Theorem to evaluate C P xydx+e'dy where Cis the path from (0,0) to (1,1) along the graph…

A:

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: Evaluate the integra ∮C -y3 dy + x3 dx for any closed path C.

A:

Q: 6. Evaluate (7xi - zk) · ndA over the sphere S : x² + y² + z² = 4 (u) by the Divergence Theorem, (b)…

A: The divergence theorem states that  ∬SF·ndA=∭V∇·FdV Where, F is the vector field, V is the given…

Q: 4. For the linear canonical system x' = Jx, x € R², determine the nature of the origin as a fixed…

A: Given canonical system x'= Jx  Case-1:-  det >0 if both Eigen value positive:- The product of the…

Q: 3. Show that the line integral 4. x + y)dx + dy C is independent of path and evaluate this integral…

A:

Q: If A = x a, – zy a,, evaluate § A · dī around the path L defined by 0 < x < 2,0 < y < 1 as shown in…

A: Stroke's theorem:         It is also known as Generalized stroke's theorem. It states that the…

Q: Sketch the grafph Following Funcfions Tor the :も L) 2=4- y bx+2y t3でンと *)モ x3+ +y2

A: Here we have to sketch the graph for the following function. i) 6x2+2y2+3z2=6j) z=x2+y2k) z=x3+y2L)…

Q: Use Green's Theorem to evaluate (y? tan- a?) dx + (3.xy+ 4x – In(y² + 4)) dy, where C is the…

A: We need to evaluate integral.

Q: 7. Use Green's Theorem to evaluate the integral f x²y dx - xy²dy where C: is the circle x² + y² = 4…

A:

Q: Parametrize the directed line segment which joins the point −2 + 3i to the point 5 − 7i, that is,…

A: The parametric equation on a line passing through the points x1,y1 and x2,y2 is given as follows:…

Q: Let M be an elliptic paraboloid z = y² + 2?. (A) "Compute the Gauss map and the shape operator. (B)…

A: Answer for sub question a: Given x=y2+z2 A parametrization is given by: Xu,v=u2+v2,u,v Then,…

Q: Let C be the shortest path that connects z to ri and /= J, (sinhz + 1)dz. Then O 1 cosh r+ n(1+) O…

A:

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

A:

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: 1. Given that z = x+ iy, where x, y are real and y #0, express z + 1 in the form a +bi where a and b…

A:

Q: 1. Construct the bisector of XY.

A: We need to draw bisector of line. AS per our guidelines we can not solve multiple questions so I am…

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: Prove that H(x, y) = (x, –y) provides a conjugacy between x' = (4 })x and Y'= (; 7). X and Y' = 1 -1…

A: Given: X' =11-11XY' =1-111Y To prove: H(x,y) = (x , -y) provides conjugacy between both of the above…

Q: Find the residues of each of the fellowing functièns at its. poles. e •f(z)- 22+3 4. ans : ri=7/4 ?…

A:

Q: (ii) Verify Cauchy-Goursat theorem for f(z) = 5 sin 2z if C is the square with vertices at 1土も-1土。

A:

Q: Find the upper bound of e²²+1 zp- (z – 1)2 + 5“ where C is the circle |z – 1| = 2.

A: The integral ∫Cez2+1(z-1)2+5dzwhere C is|z-1|=2 To evaluate the upper bound of the integral

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

A:

Q: Use Green's Theorem to evaluate | (v? – tan-1 x²)dx + (3xy + 4x – In (y2 + 4))dy where C is the…

A:

Q: (a) Solve the following Goursat problem for u(x,t): Utt = Uxx +4cos 2t, (t > 0, -t <x<t), u(t,t)…

A:

Q: now that the mapping a: E? ->E, (x,y) Coy, x + 2 ) is a transformaton and a collineation by finding…

A: One-One: Let (x1,y1),(x2,y2)∈E2 be such that: α(x1,y1)=α(x2,y2) so,…

Q: of the b) nd y- Fons c) with point.

A:

Q: Show that the following system undergo a saddle-node bifurcation. Find the vale H= Ho where such a…

A:

Q: Prove that H(x, y) = (x, –y) provides a conjugacy between 1 X' = 1 X and Y' Y. 1 1 1 1

A: We are Given that :  H(x,y)=(x,-y) X'=11-11X , Y'=1-111Y The Matrix H is corresponding to the…

Q: PLEASE ANSWER BOTH (a) AND (b) 2+2 Let g(3) = (2²-25)² (a) Locate and classify all the isolated…

A:

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

A: In R2, what is the dual cone V* if the primal cone V is V = {y1 (-3, -4) + y2 (1, -3) I y &gt;= 0}

Q: Given F=. By using Gauss's theorem, find f F ds for a paraboloid x = 4-y² - 2² with x ≥ 0 as shown…

A: We are given  F=-3x+1+z3,y+1+x3,6z+xy So, the divergence of F is div…

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

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Q: • Verify that 3r is a one-parameter family of solutions of the DE ry + y = 3r. • Deduce a solution…

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Q: Let P denote the path r(t) = (7cost), where 0<t< 2n, and compute ſpF - dĩ where F = (!+ty 4 sin…

A: Let F→x,y be a vector field and r→t=xt,yt be the path of an object, where t1≤t≤t2. The line integral…

Q: 2. 22 – x2 1 By sketching the traces on the ry-, rz- and yz-plane a.

A:

Q: b- Let X₁, X2,... X (a) Find a comp (b) Find the UM

A: Solution:   (a):

Q: 4. let f(x, y) = x² – xy + y² – y. find the direction u and Duf at Po(1,–1) for which Duf is the…

A: Given:- f(x, y) = x2 -xy+y2 -y To find:- Direction u and Du f at point p0 (1, -1) for which Du f is…

Q: Evaluate I = Se(sin æ + 7y) dæ + (3x + y) dy for the nonclosed path ABCD in the figure. А 3 (0,0),…

A:

Q: Complex Analysis

A: For given function, First we will show the function is harmonic function as shown below :From the…

Q: Consider the solid bounded by surfaces S1, S2, S3, S4, S5, and S6 with vertices A, B, C, D, E and O,…

A: In this question, we use the given sketch of the surface and find the parametrization for each…

Q: What are the perpendicular generators on (P) to 4 %3D of the surface

A: Given equation s are, x216-y24=z....1x3=y2=z-4...2 Equation of generators of the hyperboloid (1) are…

Q: Use Green's Theorem to evaluate S. axy dy + cxy dy, where C is a counterclockwise oriented…

A: Given : a=2, c=8 We have to use Green's Theorem to evaluate            ∫C axy dy+cxy dy where C is a…

Q: 2.2 Find upper bound of zp (z- 3i)3 + 1 where C is the circle |z - 3i = 4. 2.3 Use the Cauchy…

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Q: *6. Let f: R' →R be given by =+4x'z-6xyz+4y-3x'y. Is M=f-((0}) a smooth surface (2-dimensional…

A: Given, fxyz=z2+4x3z-6xyz+4y3-3x2y2 Now, writing the given function in matrix form.…

Q: 3.1 Show that upper bound of fe dz, where C is the circle |z + 4 – il = 7. z+5i-1

A: The given problem is to find the upper bound of the given complex integral over the region of circle

Q: Find the domain corresponding to the inner loop of r=1+2cos(theta)

A: The domain  inner loop of r=1+2cos(θ)  is 0,1