Q.3 (a) Show that the function u =e-2xy sin (x² – y²) is harmonic. (b) Test the analyticity of the function w= sin z Scanned with CamScanner

Q: 5. Find a function u(r, 8) that is harmonic outside the unit disk, equals f(0) = 2 sin(30) + 4 cos…

A: In the given problem we used the fact that f is harmonic on the unit circle, and using the…

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Q: 5 dr dy Suppose x and y are functions of a third variable t. If sin²(x) + cos²(y)=- and dr - 2, what…

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Q: 1 - If xy + sin(e) + arcsin Va dy sin 1 + 1 then what is the value of dz at (, 0) || a) b) 4 8 c)-…

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Q: Consider the equation below. f(x) = 2 sin x + 2 cos x 0 ≤ x ≤ 2? Find the local minimum and maximum…

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Q: (a) e3 sin 2x da sin 2r (b) x* In x d.r (c) sin r cos rdr 3. (6)

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Q: 4) It turns out the three-dimensio ball than a football. A footba a trig function like y = a cos(E…

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Q: 13. The function y = In sinx, when differentiated is? B. COS X A. cot x C. sec x D. tan x 15. The…

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Q: 10 - f sin(82) arctan(sin 4x) da integralinin değeri aşağıdakilerden hangisidir? a) O T-2 b) - 8 8(T…

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Q: 6. (a) Find a function u(x, y) that is harmonic in R2 and that equals f(0) = sin(30) + cos(40) on…

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Q: Q1: Use the Improved Euler method to find y' = cos2x + sin3x ,0<x < 1,y(0) = 1, with h = 0.25. %3D…

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Q: 2. Find (in terms of t): x = 2 + 3 sin t y = -1+4 cos t

A: Given data is : x=2+3 sinty=-1+4 cost To find the value of d2ydx2

Q: 7(e)₁² X y= » - [1-171² 2 sec- y = (tan 17 1² ² X y = [cscx]arcsin (cos.x)

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Q: 3. Find the derivatives of the following in two ways: -by evaluating the integral and…

A: This is a problem related to integration of the function. Please follow the procedure given below.

Q: (c) The displacement, x, of a particle in simple harmonic motion is given by x = cos(3t) – sin(3t).…

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Q: 1 The value of S dx at x=0 is sinx+cosx C V7 (Inv2+1) +c Cn|vZ+ 1] +c ㅇ글미VZ+ 1| + c c -공in(V2+ 1) +…

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Q: 2. Find d using implicit differentiation. Enclose final answers. dx (a) √x=y=√√√x + y = 5 (b) xsin y…

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Q: a3z a3z 5. For z = x?siny show that дудхду ay²əx

A: As per our norms we have to write one question at a time kindly repost remaining questions.

Q: of the tangent line to the graph of f(x) = 7 sin(x) + 6 cos(x) at x = in the form y = mx + b.

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Q: Find the linear approximation to f (t)= cos(2t) at t =1/2. Use the linear approximation to…

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Q: Question 2 Differentiate the following functions (i) If y= e-t sin 4t, prove that +6+2y = 0. (ii)…

A: NOTE:- AS POSTED MULTIPLE INDEPENDENT QUESTIONS WE ARE ANSWERING ONLY FIRST QUESTION FOR YOU AS PER…

Q: 10. Does there exist a harmonic function in z| < 1 taking the value 1 everywhere on |2| = 1? Is your…

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Q: 5. What is the maximum value of the transformed sine function g(x) = -2 sin[3(x + )] – 6? А. —4 В.…

A: Since you have posted multiple questions in this question which are not interlinked so I have solved…

Q: 1 1. The function Y = sin(t² )+ 4 is graphed below. Define F(x) = [, sin(1²) + - 1 dt 4

A: Given: F(x)=∫0xsint2+14dtThus, Fx represents the area under the curve y=sint2+14(a) First of all we…

Q: ii. Verify that the u = -e-Y tany is harmonic in an appropriate domain D.

A: Given that u=-e-ytany.  If u is harmonic then uxx+uyy=0.

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A: The standard equation of any sinusoidal curve is given by  y=Asin(B(t-C))+D      or…

Q: 1-Let :=x+iy then cosh(iz ) is equal to a-cos' y+ sinh' x b-cosh' y-sin'x e- sin' x+ sinh v d- None…

A: Let z=x+iy therefore, iz=ix+i2y=ix-y=-y+ix we know that  coshz=ez+e-z2 therefore, cosh…

Q: 11. Consider the four functions sin(4x) sin(5y) (a) ƒ(x,y) = - ху (b) f(x, y) = (x² + 3y²)e¬x²-y²…

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Q: Find the maximum and mini- mum values of the function. cos x 2 + sin x

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Q: - 19. Is f (x) = sinx a periodic function if so, find its period ?

A: Introduction :

Q: 7. Over the domain 0s x s2n, the equation cos(x)-sin(x)%3D2 cos(2x) has:

A: We find the solution in the following way by using trig identities.

Q: The equation implicitly defines z as a function of t. Find dz dt +² 22 - sin (5 z) = -8

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Q: 1 In order to evaluate dx, the correct substitution is V-x²–4x+21 None of these -2 + 5 sin(t) x = -2…

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Q: Where does the periodic function f(x) = 2ešin (x/2) take on its ex- treme values and what are these…

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Q: 6. (a) Find a function u(x, y) that is harmonic in R² and that equals f(0) = sin(30) + cos(40) on…

A: To find- Find a function ux, y that is harmonic in R2 and that equals fθ = sin3θ + cos4θ on the…

Q: An equation of the tangent line to the curve y = sin(x) at x = 4n/3 is y = + -(х — 4п/3). An…

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Q: 9. If f is an always positive, differentiable function and y = In (f (sin x)), what is- dy when x =…

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Q: 1 Evaluate the equation /o x² sin (xy)dydx

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Q: 2. Consider finding the root of f(x) = e"(3.2 sin(x) - 0.5 cos(x)) on the interval [3, 4], this time…

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Q: 2. Let f (x) = 3 cos(2x) – 1. (a) Find the period and the amplitude. (b) Sketch the graph of the…

A: Use function

Q: 1 find the value of so that ky"=-1 at y= For cos x- sin y=- O V3 2 4 4

A: Solution:-

Q: Q1\ Prove the left side equal to right side in the following : * L-1 (s² + a²y² - [sin at + at cos…

A: We need to show that:L-1s2s2+a22=12asinat+at cos atWe will use convolution theorem to show the…

Q: 1. Solve the hyperbolic function of the following. i Prove that coshx – coshy = 2sinh (*) sinh ().…

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