Qu:- Prove that funcdiod u = 3y - 2x -2xy-j+x* is har monic . Final funclion v such thut fc) = U+iV is análytic

Q: 4. Show that z = a' Zax if z = e-al cos(x-at) %3D

A:

Q: 15. Verify the SSS Postulate for triangle congruence by using congruence transformations. Given: XY…

A: Given: XY¯≅RS¯,YZ¯≅ST¯,ZX¯≅TR¯ To prove: ∆XYZ≅∆RST

Q: Qu:- Prove that funcdiod U = ay - 2x -2 xy-j+x* is hav monic . Firel - funchion v such thut fcas…

A: Solution

Q: a b (6) Identify all of the nonempty submatrices of A = с d

A: Given that:Matrix A = abcd

Q: 2 1-X ie 2=tny then prove that da

A:

Q: 2. Find all volves of tand u x(t,4)=0 and simultomebusly such that =0. 3. 5x-11* C.

A: Get the equations for:  fx=0fy=0 15x2-11y=0-11x+3y2=0 or 15x2=11y3y2=11x

Q: Q: Show that the functi on f:R →R given by f (x) = ax +b, where ab e R, a #0 is a bijection.

A:

Q: Prove that v = In (x- 2)^2+(y-N)^2 is harmonic in every region does not include the point (2,N) and…

A: Given v=lnx-22+y-N2 where N=44. So, v=lnx-22+y-442                                    ........1 To…

Q: of discon tinuity of the the following func Hions (a) g(x,y) = stuind %3D (b) b) f laiy)

A:

Q: Use the Cauchy-Riemann PDEs to determine all points z = x + iy ∈ C in which the following functions…

A: First separate real and imaginary components. Then apply C-R equation.

Q: det TiP M,2 be defined by -Q,X + QX + agX ). Show that ī is a linear transforimation and find T…

A: The solution is given as

Q: 2) Prove that the foll owing func tion is not differen tiable at (0,0). 2. 2. f(x.y) = (X.y) = (0,0)…

A:

Q: Use the Wronskian and any needed theorems to show that f1 = sin x + 2x2 and f2 = e3x are linearly…

A:

Q: Q1. Verify Euler's theorem for the homogeneous funetion, fxy.2)-axy +byz + czu

A:

Q: A) Show that the surtace x-2yz ty' =4 is orthogon al to any of the sm tamily of sur faces…

A:

Q: z is a complex variable z=x+iy pic attached with question

A: To analyze and classify the singular points of the given function of the complex variable z

Q: Find the rank of A= = xS+ x + invertible. [exham S] O A MOITERUD 225 10-4 and explain why it indic 4…

A: NOTE: Refresh your page if you can't see any equations. .

Q: 요2s A) for F- 2K1-3y3+ K %3D prove That divc curl È)=0

A:

Q: 3) suppose fle) is a defferentiale funchou on the interval E-7,1J Such that H-7) =4 and fli)=1.…

A: Given, A function f(x) is a differential function on the interval -7,1 such that  f(-7)=4 andf(1)=-1…

Q: Let po) - X In (x) , using the following approx im for the secoud denvative fcxo) = FOXO -h)-ZR…

A: Introduction: Apart from differentiating a function analytically, the derivative of a function can…

Q: 1. Show that sinz is unbounded on C and lyl <|sinz] <ebl z=x+yi € C. for

A: Given:         We have to show that sinz is unbounded in ℂ and y≤sinz≤ey   for z=x+yi ∈ℂ Function…

Q: Prove that Lim + Tene + …+: 1 %3D ... 2n²+1 V2n²+2 2n²+n.

A:

Q: 3. Use Green's Theorem to evaluate G³ï+xj)•dr around the perimeter of the rectangle 0<x<2,0<y<3.…

A: Given ∫C(y2i+xj).dr We know that dr = dxi+dyj Thus ∫C(y2i+xj).dr = ∫C(y2i+xj).(dxi+dyj)  =…

Q: :- Prove that funcdion U = 3y - 2x -2xy-j+x is har monic . Final • funchion v such thut is andilytic…

A: Given function: u=x2-y2-2xy-2x+3y

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: graup Consider a dibedral 2. Du= carb: d=b-(ab)"%=D1> Discuss all passible Commulators 'and verify…

A:

Q: hat subring R[x², x°] not isomorphic to R[x].

A:

Q: ☺ show dhat 2) G(x,x) => Uola) Uorlo) were G is green funcfion

A:

Q: 2 / The eanation rasine itis an e quation of acircle passing through the origin and center onthe X.…

A: Polar to cartesian conversion:

Q: a sondom Semple XSI .Detemie a clistrbutian with Size n Conider (df F(m) =1 -x² Sei juences has…

A:

Q: carulate the aistance between pointS k=(0,9) and . G7= -6,6) inthe.coordmate Diane. mo0 Cnuer :…

A:

Q: 6) let fl2) = CosCitaiy) 22atey Express flz) that f satisfies in the form and fornd z So the Canchy-…

A:

Q: Show that the IVP x" = -6x(x')3, x(-1) = -1, x'(-1) 1/3, has a unique solution x and find the…

A: Introduction: An initial value problem is a differential equation whose solution is the curve…

Q: prove that the Lollowing examples satisly Laplace eqadion are -2y Cos 2X

A:

Q: z? f(2) = 1-z* 4

A: We use the fact that the 1/(1-z)= 1+z+z2+z3+z4+......

Q: Find the Zero and its order for the funcation fcz) = 1 -Pit z te.

A: We know that, f(z) = (z-z0)n has zero of order n at z=z0, if f(z0)= 0

Q: Give an ezample of a funtion fi (a, o)=(-0,0o having all three of the following propenties for 2<0…

A:

Q: - Pcosø prove that dw xy is Cont s Lony) - the fun ction (-1, 2) = x*y+z and x = PSinf cse y=pSi- -…

A:

Q: If the Wronskian of f and g is t cos t - sin t, and if u = f+ 2g, v = f - g, find the Wronskian of u…

A:

Q: prove that Sa/Gn has f discription with M-ly ny-l Degrees tof freedom

A: Suppose that xi and yi are two random samples of size n, drawn from a normal population.  Population…

Q: If F G) and g(x) are conbinuous on [anb] andit =Sprove thab. SF= 58 prove thab Icefanb] Such that…

A:

Q: The function u, takes on the following values : 1 1 1 1 1 u, = , u. + .....u, 10 1 + 3+1 + 32 +…

A: SOLUTION-

Q: If C, Cz - Cn are Constovts 2111 . u,), uzX2) ---- Un (X)ave Livffen antiable 4111 funetions at x…

A: Introduction: Differentiation is a property of a real-valued function. When the independent variable…

Q: -3z2-3 Let C: |z – i| = 4 and I = f. dz. Then %3| z2-1 I=2ri |=0 by Cauchy-Goursat Theorem |=0…

A:

Q: #04 Check thet the funetions 7,g and h are linearly dypendint oY independent 7 f(1)- é, g)=ë, kp-t…

A:

Q: 2 - Find the inter val on which f are Con Cave down and infleobion Points a -y = x2 5X+10 6- ソ= (¥+…

A:

Q: 3)suppose fle) isadifferentialle fmehon on the intervall E-7,J Such that Hl-7) =4 and fl)=1.…

A: Intermediate value theorem

Q: What is thie generalized union and interdection of %3D where 1-10,1)

A: As given,  λ is the index set for A.  Hence, there are two sets possible,  Aλ=0  =  [ -(1/0) ,  0]…

Q: 6. Find an explicit function f: [0,1] and prove why it is (0, 1) that is a → bijechove bijection

A:

Q: Q)is a) x^2=y^3 reflexive antisymmetric Transitive  Explain it correctly,solve only when know…

A: We have to find the correct option