show that the. following Complex functron is dis continuous at z=i. fCZ) = スー! %3D 3.

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

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Q: Let w = where z = ret®. 1) Show that by using Cauchy Riemann Equation (C.R. Eq.) in polar form that…

A: See the attachment

Q: Is the function eiz² holomorphic in C? Explain why. What are the Cauchy-Riemann equations for eiz?

A: Given function : f(z) = ei z2

Q: Sketch the strophoid shown below. r= sec(0)- 2 cos(8), -<0 < x/2 1.0 1.0 0.5 0.5 -10 -0.5 0.5 1.0…

A: A strophoid is a curve generated from a given curve C and points A (the fixed point) and O (the…

Q: The speciat sotution to the equatio %3D ho A/y)=+X B/yo)=y - %3D d/other than that

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Q: Find the parametric equation for a line that is tangent (intersection) of the two fields below: −2x…

A: We have to find parametric equation for a line that is tangent (intersection) of the two fields…

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

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Q: Use the IVT to prove that the curves y = x2 and y = cos x intersect.

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Q: 7. Derive the orthogonal trajectories of the family of hyperbolas xy = c. %3D

A: The solution are next step

Q: 3. Use the theorem in Sec. 44 to show that La (z-zo)"-1 dz = 0 (n = ±1, 12,...) when Co is any…

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Q: Let f(z) = z2 is f(z) satisfy Cauchy-Riemann equation ?

A: Let any complex function f(z) = u + i v then it satisfies Cauchy-Riemann equation when 1) ∂u∂x=∂v∂y…

Q: A funchion is defined by +the formua a f(x)=Ź ) which of the follauing is the %3D value of

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Q: It is easy to see that u(z) = Im (+) is harmonic in the unit disk |2| <1 and lim,→1- u(reio) = 0 for…

A: Given, Uz=Im1+z1-z2,z&lt;1 Now,…

Q: Show that the path given by r(t) = (cos t,cos(2t), sint) intersects the xy-plane infinitely many…

A: Consider the given path rt = cost , cos2t , sint  Then, xt=cost , yt=cos2t , zt=sint

Q: Find three different parametrizations of the graph of y = x3.

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Q: What is the order of the pole of f(z) = 1 (2 cos z −2+z²)² at z=0? [HINT: Work with 1/f(z).]

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Q: Find an antideriuative Flx) of the functian f(x) = 8 sinx such that FlO)=D1 %3D 13 + COSX

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Q: Find the exact value of | (yi+ vxj) · dr where C is the parabola y = x² from the origin to the point…

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Q: The Cauchy-Riemann equations for f(z) is

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Q: 3. Consider the ra greater across z =1-r² - y² plane and the s and a paramet

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Q: Show that the function f(z) = e-z",z # 0 and f(0)=0 is not analytic at z=0, although Cauchy-Riemann…

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Q: function holomorphic in 2 except p in an open neighborhood of w, the

A: To prove, ∫Tf(z)dz=0

Q: za z = e

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Q: Cannot solve

A: Multiplying and dividing first term by secx and second term by tanx of left hand side of equation ,…

Q: dz - Prove that : Iz%3D2 %3D z%3D2 z+1 2in.

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Q: Express the given parametrization in the form y = f(x) by eliminating the parameter. x = 5t + 2, y =…

A: Given

Q: show that fGx) = C,ex +C,e* s a solution to y for all real conatanto C, +C2, and then find C,, C,…

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Q: Show that (d/dz)ž does not exist anywhere, i.e., f (z) =z is non-analytic anywhere.

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Q: Describe the bifurcation for the following dy - Ay - y %3D dt

A: The saddle node-bifurcation: Let y˙=f(α,t) is the system of equation, the to find the saddle-node…

Q: show that the. fallowing Complex functron is dis continuous at z=? 121 1 fCZ) = スー! %3D 3. %3D

A: Topic:- limit and continuity

Q: Find the arclength of y = 2x /2 on 1 < ¤ < 3 2x3/2 uostion

A: given that y=2x3/2. we need to find the arc length in the interval [1,3] the arc length formulae is…

Q: Use the comparison theorem to investigate whether the spiral r=1/θ starting at θ= 2π and going on…

A: Given spiral is r=1θ. We have to use comparison theorem to state whether the given spiral has finite…

Q: Draw a sketch of the cylinder z = -4 - y2.

A: A cartesian coordinate system contains two mutually perpendicular number lines named x-axis and…

Q: Show that the Euler-Cauchy Equation ry" + ary + by = 0, r+0 can be transformed into the constant…

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Q: Find the areas of the regions Inside one loop of the lemniscate r2 = 4 sin 2θ

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Q: Is h: (-1,1) → R, h(x) = tan[(t/2)x] homeomorphism? Please search. 14:42 / %3D a

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Q: Show that the function f(x + iy) = Vlæ|ly| satisfies the Cauchy-Riemann equations at the origin but…

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

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Q: Show that UV=12 given, UX = 8, and XY = 10 using the intersecting %3D Secant-Tangent Theorem. * U

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Q: iven that use the bhi tzS to compute %3D irst shifting Theorem [e"e cos 7+]

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Q: Find the surfaces on which the function u = 2 (x2 + y²)/z is constar

A: Since u is a constant so, x2+y2z=4a , where a is an arbitrary constant.

Q: Determine if the function satisfy the Cauchy-Riemann equations. 5. f(z) = z?

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Q: Find the tangent plane to the elliptic paraboloid z = x² – 2y at the point (1,1,1). - O A. z = 2x –…

A: Given that: z=x2-2y2      and point is:   (1, 1, 1)

Q: 13. Point P is the centroid for AMNO. Calculate OQ if ON = 17. Round to the nearest tenth if…

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Q: Express x = In(3t), y = 5 – t in the form y = f(x) by eliminating the parameter. %3D y =

A: Given that x=ln(3t) and y= 5-t we need to write y=f(x) by eliminating the parameter  Now , x= ln(3t)…

Q: flz) = Im z is continuous %3D

A: The objective is to check f(z) =Im Z is continuous Or not.

Q: %3D %3D In MIMI2 9.5. Ly=, Wq= F and L== au Find : Po =? and P,= ?

A: A/B/c Queueing System: A is the interarrival-time distribution. B is the service-time distribution.…

Q: Find eauation of ny Perbola at o Ne tne foci Fz the and crankshafto f Fi Fz ny Perbola= Fi F

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Q: Show that f (z) = e? is not analytic using Cauchy-Riemann equations.

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