Prove that the following functions u/v are harmonic; then find the conjugate harmonic function v/ u. Express u + iv as an analytic function of z. 1. u = ln(x² + y²) 2. ve sinx

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Q: f(x) = 120x0.80

A: You must have an idea about basics of derivative in order to understand this problem.

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Q: (g) Plot the following set in the complex plane: {z EC ||z- (1 + i)| ≤ √2} U {ze C| Im z>2}.

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A: Order = highest derivative order = 2

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Q: 1 If f(x) = compute f(2) and f'(2)

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Q: 1 S dx = 3x+2 0-²(3x + 2) + C O 2√3x +2+c 3 O²(3x + 2)² + C A O√3x + 2 + c

A: The given integral is: I=∫13x+2dx  ...1   As we know the Power Rule: ∫xndx=xn+1n+1+C ; n≠-1

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Q: P2: Calculate the volume of solid of revolution when the region bounded by y = √√x + 4 and x - 2y +…

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A: Concept: Exact differential equation: For the differential equation of the form Mdx+Ndy=0 If ∂M∂y=…

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Q: 18. Up to what derivative is the derivative of y = x6 + 2x5 - 4x4 + 7x³ becomes 0.? a. yv b. yu c.…

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Q: integrate [(x csc^2 (2x) - x cos (2x)] dx

A: Given problem:-  ∫ [(x csc2(2x) - xcos(2x)] dx

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Q: A cylinder shaped can needs to be constructed to hold 200 cubic centimeters of soup. The material…

A: Given problem:- A cylinder shaped can needs to be constructed to hold 200 cubic centimeters of soup.…

Q: Consider the following initial-value problem. y ′ + 3y = e−3t,    y(0) = 5 Take the Laplace…

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Q: above function is a solution of which of the following differential equations? y' = y² y' = y y' = 1…

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Q: e²x 9e2 + 18e + 10 (d) / 5 dx

A: To evaluate: ∫e2x9e2x+18ex+10dx Substitute ex=u⇒exdx=du:…

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A: Let's evaluate given integral.

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Q: Find the derivative of the following exponential and trigonometric functions: please attach your…

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Q: An object moving in a straight line travels s(t) kilometers in t hours, where s(t) = 8t² + t. (a)…

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Q: 3x+5 Find S dx (Using substitution method). √3x-7

A: This question can be solved using the concept of integration by substitution.

Q: Find f'(x) where f(x) = esina Of(a)=esing cos O f'(x) = sinx. ecosx ○ f'(x) = ecos sinx . O f (2) =…

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Q: 1) Find the equation of the tangent line and normal line to the graph of the function y=x√√x-1 at…

A: As we know that; The expression for the equation of the tangent line is: y-y0=mx-x0 Where m is the…

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Q: Find the regions where sinx sx.1

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Q: TT sinx sin 2x dx 2 cos x

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Q: A spherical balloon is inflated with gas at a rate of 800 cubic centimeters per minute. (a) Find the…

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Q: Evaluate: lim 1+ O 1 a 00 none of the choices In aª (A)

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Q: 4. Which of the following is an exact DE? A. (x²+1)dx-xydy-0 B. xdy+ (3x-2y)dx = 0 C. 2xydx…

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Q: Solve 2 cos² (x) - 3 cos(x) + 1 = 0 for all solutions 0 ≤ x < 2π X = Give your answers as a list…

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Q: P1: Calculate the area bounded by the curves: A. y = x² and y² = x.

A: Since you have posted multiple questions which are not interlinked i can do first question(area-A)as…

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Q: On your own, verify that the indicated expression is an implicit solution of the given first-order…

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Q: Find the median of 65 70 65 62 64 73 67 60 50

A: Follow the procedure given below.

Q: Find f(t). ℒ−1{(2s + 7) / (s2 + 8s + 65)}

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Q: Differentiate f(N) = (N) = 0 bN² + N with respect to N. Assume that b and K are positive constants.…

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Q: A cardiac monitor is used to measure the heart rate of a patient after surgery. It compiles the…

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