z is a complex variable z=x+iyShow that f(z)=((z^2)+1)/((z^2)-3z+2) is continuous for all z outside |z|=2

Q: Use Green's Theorem to find f. [(2x – y+ 4) dx + (5y+ 3x – 6) dy] around a triangle in the xy plane…

A:

Q: biven that y=sin(3lncx)) is a solulion of x y" + xy' +9y=0, solue x y"+ xy' +qy=0 ; y()= 2 =y'().

A: Solve Cauchy Euler differential equation

Q: The curl of- yi+z+xR"

A: In this question, we find the curl of the vector function by using the determinant method.

Q: 7. Sketch the surface 15zs9-x' - y² and x'+y' <1

A: To find:

Q: then show that u and v satisfy the Cauchy-Riemann equation everywhere for ( i) and for all z # 0 in…

A:

Q: 2. Find the coordinate of the points on the cardioid r=1- cose at which there is a horizontal…

A: We are given the polar curve: r = 1- cosθ use formula:         x=r cosθy=r sinθ then,  dxdθ=-sinθ+2…

Q: Find div F and curl F if F(x,y,z) = x³i - 6j+yzk.

A:

Q: 2- find if z = x + 2メッ ze %3D U COSU = u sinv

A:

Q: Sketch the graph of x=z^2 in the xy plane (2d context) and xyz space (3d context)

A: 2d graph of  x = z^2

Q: Qss- Prove that fcz) = cx=y') + ( are harmonic function of C, y) ,but are not . hormonic conjugates.

A:

Q: A The roots of Characteristic equetion f oreler, lineor homopeneous-equation with constant…

A:

Q: Find div F and curl F if F(x, y, z) = 10y³zºi – 8x³z¹ºj – 5xy³k. div F= curl F=

A:

Q: Two functions u and r of x and y are said to satisfy the Cauchy- Riemann equations if u, = v, and u,…

A:

Q: Find the equation of the tangent line to the curve of intersection of the surface z = x² - y² with…

A:

Q: what is the area of the rotational surface formed by rotating the part of the function y= x^3/3…

A: We apply the above formula to solve this

Q: Find the points on the cone z2 = x² + y² that are closest to the point (1,-1,0) %3D

A: Given that, z2=x2+y2 and the point is (1, -1,0). Form the equation of distance as follows.…

Q: 2. Consider the function f(z) = where z is a complex variable defined as z = x + jy. nvestigate…

A: Given: The given function is fz=1z we want to check that whether given function is analytic or not…

Q: (a) S,(Iz – il2 – z) dz along the semicircle y = 1+ et“, 0 < t < n; -

A: ∫γz-i2-zdz=∫0π1+eit-i2-1-eitieitdt=∫0π1+cost2+sint-12-1-eitieitdt=∫0π1+cos2t+2cost+sin2t+1-2sint-1-e…

Q: Use Stokes's Theorem to evaluate F dr, where F(x, y, z) = x²i+z²j-xyzk and S is z = /169-x -y . Use…

A: The given problem is to evaluate the integral using stokes theorem, we have to convert the line…

Q: Find the orthogonal trajectories of the family of circles with center at the point (0, 1) and radius…

A:

Q: Find an equation for the tangent plane to z-x-y = 3 at the point (2, 1, 8) Z - ) %3D

A: given z-x2-y2=3 at point 2,1,8

Q: Differentiate, and make sure to show all your work: y = exin(2z) %3D

A: The given question is taken from the derivative of the function in which we have to find the…

Q: 1. A such that the difference in distances between (x, y) and two fixed points (called is the set of…

A: A___ is the set of points (x, y) in a plane such that the difference in distances between (x, y) and…

Q: 4th degree polynomial of y=sinxcosx centered at x=pi

A:

Q: za z = e

A:

Q: Find the number of zeros of f(z) = 2z* – z + 5z – 1 in the annulus 1 < |z| < 2. %3D

A:

Q: Which of the following is the least distance from the point (2, –1,1) to the plane x + y – z = 2?

A: Given: The plane equation is x+y-z=2and the distance from the point is 2,-1,1 To find the least…

Q: A) Integrate f(x, y) = xy^2 over the square bounded with endpoints at (0, 0), (0, 1), (1, 0) and (1,…

A:

Q: Use cross products to find the area of the triangle in the xy-plane defined by (1,2), (3,4), and…

A:

Q: Find the appropriate parametrization for the given piecewise smooth-curvein R^2, with the implied…

A: Here, a semi-circle is of radius 3.

Q: Let F = (2yz – 3x) i + (3xz + 3y) j – (2xy+ ∞z) k. Find div F and curl F.. |

A:

Q: Find all points in the xy-plane with integer coordinates located at adistance 5 from the origin.…

A:

Q: Show that the function f defined on [0, 1] by the conditions f)=2rx when <,r=1, 2, 3,. 1 1=1, 2,…

A:

Q: -axis. 5. Evaluate dV, where E is the solid tetrahedron with vertices at (0,0, 0), (2, 0, 0),…

A:

Q: 9-x²-y² is the upper √y half of the disc centered at origin with radius r = 3 The domain of f(x, y):…

A:

Q: Find y': %3D Oy =- Oy=--

A: A detailed solution is given below

Q: Find all possible bifurcation points and their types (analytically and/or graphically). dr (a) =r -…

A: Since you have posted a question with multiple subparts, we will solve the first three subparts…

Q: Find the tangent plane to the equation z 2y cos(3r - 6y) at the point (6,3,6) %3D

A:

Q: Q3A) Using Cauchy Riemann equations show that: f(z) = 2z8z5 + 4z6 4z38z² + 2z is analytic in…

A:

Q: fer) sen ax %3D

A:

Q: 1+iz if w= Find the image |z|<1 1-iz

A:

Q: 3- Verify the properties (HINT Use integration by parts) F[ux] = iF[u] F[uxx] = -²F[u]

A:

Q: Find the families of characteristics of the PDE (1-x²)w„ - u,, = 0 in the elliptic and hyperbolic…

A: Pde

Q: What does parseval's identity imply about relationship between the dot products x · y and [x]ẞ·…

A: Concept: A branch of mathematics which deals with symbols and the rules for manipulating those…

Q: Find div F and curl F if F(x, y, z) = xºi-7j+yzk. div F= curl F=

A: Given that F(x,y,z)=x6i-7j+yzk. The objective is to find divF and curlF.

Q: derivatives of u, v and w with respect to x, y and z, and use them to compute Jacobian Obtain the…

A:

Q: 4. f(z) = { |z|* z = 0 verify that the Cauchy-Riemann equations are satisfied at the origin z =(0,0)…

A: