Q3 Verify Green's theorem in plane for (x² - 2xy) dx + (x²y + 3)dy where c is the boundary of the region defined by y² = 8x and x = 2

Q: ii) Solve the differential equation (D² - 5D +6)y=x²e³x D = -

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Q: Solve the equation. Give your answer correct to 3 decimal places. 81 100 100e e-0.03x X =

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Q: Question 1 T(₁,2)=(-221-22, 21-22. determine if T is invertible. O The standard matrix of Tis A = ^=…

A: Given linear transformation is T(x1, x2) = -2x1-2x2, 2x1-2x2

Q: ) Let V be a vector space over any field F: (a) Prove that V is infinite dimensional iff there is a…

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A: Continuity of the function

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A: We have here Score  x Frequency f f⋅x Cumulative frequency cf 0 14 0 14 1 19 19 33 2…

Q: Solve the given differential equation by undetermined coefficients. y"-9y=(x²-4) sin(3x)

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Q: (a) Suppose X U (0,n), where n is a positive integer X-[X] U (0, 1). (b) Use the result of (a) to…

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Q: Compute Y (II) withe y" y'= -8 (Sinx+cosx. Y(T) = 0, y¹ (F) --8, by @ Taylor Series

A: Given differential equation is y''-y'=-8(sinx+cosx)     (1) and y(π)=0, y'(π)=-8 Solution a: Using…

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Q: Find the cost function if the marginal cost function is C'(x)=8x-3 and the fixed cost is $12. OA.…

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Q: a) x^3 - 1,2x^2 - 8,19x + 13,23 = 0 has a double root close to 2. Determine the root of this…

A: As per company guidelines we are allowed to solve one question at a time so i am solving first one…

Q: Express the following as a linear combination of u =(3, 1, 7), v = (1, -1, 4) and w= (18, 7, 8).…

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Q: A person invests $100 today and $200 twenty years later. Interest is credited at a nominal interest…

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Q: 2. Let X denote the reaction time, in seconds, to a certain stimulus and Y denote the temperature…

A: Given: Joint density of two random variables X and Y is fx,y=1.5x2+y2,  0≤x,y≤1          0,…

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A: please comment if you need any clarification. If you find my answer useful please put thumbs up.…

Q: 7. x' = 1 1 1\ 2 1 -1 -8 -5 -3 X

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Q: Let I = (π, π) be the open interval and consider the R vector space Diff (I, R) = {f: I → R : ƒ is…

A: Please see the attachment

Q: Use graphing paper to plot the following points then connect the points as coordinates.  A. a.…

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Q: Obtain the general solution. (D4 + 4D³ +2D²-8D-8)y=0 O y=e²x(C₁+C₂x) + C3е√²x + С₁е-√²x Oy=e-²x(C₁x…

A: Given differential equation is D4+4D3+2D2-8D-8y = 0

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Q: Let A = {5, 6, 7, 8, 9}, B = {7, 8, 9, 10, 11}, and C = {6, 9, 11}. a. Find An B. b. Find AU B. c.…

A: Given: A={5,6,7,8,9} B={7,8,9,10,11} C={6,9,11}

Q: Assume there is a certain population of fish in a pond whose growth is described by the logistic…

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Q: Use the composite trapezoidal rule with the step length h = 0.1 to evaluate sin x = 5.² in six…

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Q: Find the sum of the series. e -8x² Σ (−1)n 87x6n n = 0 n! X

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Q: f(n)=4n²+5n²*log(n) Show that f(n) is O(g(n)) for g(n) = n³

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Q: The indicated function y₁(x) is a solution of the given differential equation. Use reduction of…

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Q: v) Solve the following differential equation by using Laplace Transform technique. d²y(t) dt² +y(t)…

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Q: 5) f(x) = ²-4 x-2 4 if x # 2 if x = 2 Is f(x) continuous at x=2? Sketch the graph of the function.

A: (5) Solution:- Function can be written as :- Continuity of x2-4x-2:x<2  or   x>2, &  4  :…

Q: (x + y - 4)dx - (3x - y - 4)dy = 0; when x = 4, y = 1

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Q: 1. Let S = {(1, 0, -1, -1),(1, -1, 1, 2), (5, 2, -9, -11)} CR¹. a) Show that S' is linearly…

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Q: Determine to and the Values of sake following y PDES elliptic, parabolik, or J hyperbelic tho + X…

A: Let us consider the PDE of the form a∂2ϕ∂x2+b∂2ϕ∂x∂y+c∂2ϕ∂y2=0 Determine ∆=b2-ac The PDE is…

Q: ·[²₁₁-²² Compute (a) Trapezoidal rule de using the

A: Given integration is I=∫-11e-x2dx here f(x)=e-x2 For n=2 subinterval step size is h=1-(-1)2=22⇒h=1…

Q: Solve the initial value problem. √y dx + (x-9)dy = 0, y(10) = 1

A: Sol:- ydx+x-9dy = 0 , y10=1It can be rewritten as :-ydx=-(x-9)dy

Q: Tutorial 13: Heaviside's formula Confirm that the following functions have simple poles and use…

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Q: Write out the beginning and end of the argument if you were to prove the statement, "For all numbers…

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Q: 16. T (c)T(d) = T (c+d). 17. If the n x n matrix A is a product of elementary matrices then the null…

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Q: 0 (2x-√√x) da

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Q: 7) Find all complex solutions to the equation below. Express your answers in both polar and…

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