Vn+ cos n lim Vn +1 1. Evaluate with proof, using the Squeeze Theorem: 2-0

Q: no 2n? -5 sin( n) d] lim %3D 3. Prove or provide a counterexample for the follow

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Q: Let F(x, y) = x2 + x² + y2J- (a) Show that F. dr +| F. dr if C and C2 are the semicircular paths…

A: The function given to us is  F(x,y)=yx2+y2i-xx2+y2j

Q: Evaluate using the Squeeze Theorem.

A: The squeeze theorem states that let g(x)≤f(x)≤h(x) for all x close to a but not equal to a. Now, if…

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Q: (4)using the relation F= Vn show that J1(x) cos x %3D

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Q: Q2= A) for E= 2xĭ-3Y3+K %3D prove That divc curl È)=0 %3D

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Q: The conjugate harmonic function v(x, y) of u = In (x² + y²) is

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Q: R4 for g(x) = cos(xx) on [0, 1]

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Q: b) f(x) = cosx on the interval [0,] %3D

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Q: 3. Verify that u(x, y) = x² + 4.x – y² + 2y is harmonic and find %3D - a) the harmonic conjugate…

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Q: J32 For z = cos(x-4y) show that # дудхду 332 дугах

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Q: 3. Let z = x + iy. Prove that the function f (z) = e-* sin y – 10 + ie-* cos y is analytic in C AND…

A: analytic  function

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Q: Given a function f(x,y,z) = (x+3) In (6y - 4) sin (10z). Find the domain of the function. %3D а. (…

A: Domain - values of variables (x,y,z) for which the function is defined.

Q: Q4: (a). Prove that u = 2x(1-y) is harmonic.

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Q: (a) Define the symbols ôf/DE and af/dz by af 1 (af 10f 2 (dr af 1 (of 18f i by, dz 2 dr' i dy as…

A: Since you have asked multiple questions, we will solve the Question (a) for you. If you want any…

Q: Find the Wronskian of the functions f(t) = et sin(t) and g(t) = et cos(t). NOTE: Your answer must be…

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Q: 6. Let f(r) = -a cosr. With po = -1 and p1 = 0, find p3; %3D

A: f(x)=-x3-cosxp0=-1p1=0To find:p3=??

Q: ldéntities will prove useful in achie Exercise 12. Show that E, (T: – ¤) = 0 %3D | E (*: – µ)² = E…

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Q: F(X)=JX F: [o,2]-> show i fis lipschit z funcla or not find k to

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Q: What is the Wronskian for y" + 3y = In x? & W 3 b. W = 3 c. W = V3cos 3x-V3 sin V3x d. W 3 cos 3x -3…

A: Here, the characteristic equation is m2+3=0. So,                         m2+3=0⇒m=±3 Thus, the…

Q: -Consider the function defined by the base: Find dz ) Prove that дz +y əx дz ду = sin 2z z =…

A: Topic:- application of derivatives

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Q: Let a > 0 be real. Use residues to evaluate the princi- pal value of the integral R 1+ cos ax lim…

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Q: O i using The( 3) uence Xm>is

A: First we have to show that Given sequence is monotonic and bounded then it is convergent

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Q: If f : (0, 1] → R is defined as if z is rational I if z is irrational. S(x) = %3D cuss the Riemann…

A: Here the f is bounded on [0, 1]. Let Pn be the partition of [0, 1] defined by Pn = (x0 , x1, x2, ……

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A: Given :          F→ = 2x i - 3y j + k   To prove that div(curl F→ ) = 0

Q: ▼ 3.1. Use Cauchy-Riemann equations to prove that ƒ(z) = z² is differentiable at z = zo E C.

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Q: 1 - Show that u(X, y) - e^Cosy is harmonic function = e and Find tne Conjugate harmonic v(X,y) and…

A: Harmonic function

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Q: 2- Show that the function U(x,y)= 3x²y-y² + y is Harmonic and then find it's Harmonic conjugate V(x,…

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Q: (등공) of and ôf Evaluate for f (x,y) = sin (3 x- 2y) at 36

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Q: Prove that arctan x + arctan y = arctan(x + y) / (1 − xy),  xy ≠ 1.                   Use the…

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Q: 22=2+4i Let e = [4 Im (z) + 2 Re (z)] dz 21=0 where C the parabola y z1 to z2 . Evaluate 3Re (€) .…

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Q: Defn `x;>-` "x; diverges to minus infinity" VR>O such that Vj >Ng *;<-R NR HWs If x→0 then → O.…

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Q: Express the limit lim (3 cos (2ra* ) + 4)A¤¡ over [6, 8] as an integral. 2 CoS n- 00 i=1 9. Provide…

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Q: in order to find c2. Let f"(x) = 6x – cos x, f'(0) = 2, and f(0) = 5. Find f(x). (b) %3D %3D 0(10) A…

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Q: II. f(t) = cos t, lim h

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Q: The conjugate harmonic function v(x, y) of u(x, y) = In (x2 + y2) is *(;) + -1 1. 2tan () + -1 2tan…

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Q: HiW Q Prove that : tanhclax) = x-! %3D x2+1

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Q: 9: Find the Zero Cnd its た Aunction fに)、1にかi+Z+を。 Oroler

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

Q: 1) Evaluate the following limits. cos r - x4 - 1 sin? 2x 3* + cos r a) lim b) lim -00 3+2 – 2* c)…

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Q: Find the Wronskian of the functions f(0) = cos²(0) and g(0) = 1+ cos(20). NOTE: Your answer must be…

A: Given: f(θ)=cos2(θ)  and  g(θ)=1+cos(2θ) To find: Wronskian of f and g i.e., W(f,g)(θ). We know that…