Q1(a) A function y = f(x) is given by the following table of values. Make a harmonic analysis of the function in (0,6) up to second harmonics. 0 X 1 2 3 4 6 5 4 8 y 15 7 6 2 4

Q: = Find the general solution of the following PDES. LO • з Их + 2 Иу ansg- и(x,y) = не , u(x,0) = чех…

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Q: (d) The set {(x, y) = R² | y 0} is empty. ( ) (e) If A is a subset of B, and B is a subset of C,…

A: According to our guidelines we can do at most three sub-part of a question at a time. So please post…

Q: 3. If $1000 is invested at 10% compounded continuously, the future value S at any time t (in years)…

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Q: 4. Use Cartesian coordinates to set up the iterated double integral given by Iff v² av D where D is…

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Q: hat is grap

A: First of all, in graph there should be one edge from a typical vertex to another vertex. In brief, a…

Q: 5 By separation of variables, Solve the following PDES :: ²4 ²4 dt² dx² 0 o , u(e,t) = u(5,t) =6…

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Q: • show that (x, y, z) = PDE : 2² + 8²4 дуг дуг + 2 x² + y² + z² = 0 824 dz² satisfies the

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Q: F:1: Solve 12(s+10)-140 (s+1)² +400)

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Q: - x, then answer the following (1) Find the function's domain (2) Find the function's range. (3)…

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Q: if f:[0,2] 3 R such that if x>0 f(x) = { ²2 if x<0 show that whether f is continuous in [0,2]

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Q: 1. Consider the differential equation: y" - 3y' + 7y = f(t), such that y(0) = 0 and y'(0) = 2. The…

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Q: QUESTION 4 Calculate the area between y = 7 - x² and x-axis from x = -1 to x=2 as shown in Figure 1.…

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Q: Find the differential dz of the function f(x, y) = 4y² + x²y-2xy and use it to approximate Az at…

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Q: 4 Find the general Solution of the following PDES -X • 3 Ux + 2 Uy =o UCX, O) =4e 2 (3y-2x)/2 ans-…

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Q: Gauss - Jordan Elimination Equations: -3x + 5z -2=0 x + 2y = 1 - 4z -7y=3

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Q: Let L(y)=(x-1)y" - xy + y a) with the observation that y, zx is a solution of L(4)=0 on (1,00), by…

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Q: Integrate f(x,y,z) = x + √y-2² over the path from (0,0,0) to (4,16,4) given by C₁: r(t)=ti+t²j,…

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Q: Jff v² av where D is the tetrahedron in the first octant bounded by the coordinate planes and the…

A: Let us consider the given integral I=∫ab∫f(x)g(x)∫p(x,y)q(x,y)F(x,y,z)dzdydx To solve the triple…

Q: A. Direction. Write the characteristics of inductive and deductive reasoning by completing the Venn…

A: A. Inductive reasoning:- Inductictive reasoning is a bottom up approach. It takes us from specific…

Q: Solve the following system 2x₁6x₂x3 = -38 -3x₁ - x₂ + 7x3 = 34 -8x1 + x₂ - 2x3 = 20 using the Jacobi…

A: Given system is 2x1-6x2-x3=-38-3x1-x2+7x3=34-8x1+x2-2x3=20 We can write it as x1=-1820-x2+2x3…

Q: To find how much heat is required to bring a kettle of water to its boiling point, you are asked to…

A: See below Lagrange interpolation method.

Q: Let p= "It is extremely humid." Let q = "It will rain tomorrow." Convert into symbols: "If it is…

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Q: 5 Solve the differential equation (7-1) + x² ) dx + (1=x√x) dy=0

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Q: Use Cartesian coordinates to evaluate Jff v² av D where D is the tetrahedron in the first octant…

A: Let us consider the integartion I=∫ab∫f(x)g(x)∫p(x,y)q(x,y)F(x,y,z)dzdydx To solve the integral…

Q: In each part, solve the linear system, if possible, and use the result to determine whether the…

A: We have to solve the linear system and use the result to determine whether the lines represented by…

Q: By direct partial integration, Solve the following PDES 8- 8²u axdy = CBX COSy? SXUCX,H) EX? ₂ U (#₂…

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Q: 7) A can of soda with a temperature of 56 degrees Fahrenheit is placed in a refrigerator which is…

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Q: 1. Use de Moivre's theorem to find all solution to 25 +32 i = 0. Give the solutions in polar form…

A: Note: According to Company Guidelines we are providing the answer of first question. Kindly post…

Q: Find the innverse of the matrix b: 5 0 6 9 1 2 3 4 9 3 5…

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Q: Find and classify the critical poruts g a te functions f(x,y) = exsing f(x, y) = excosy

A: 1 Given function is fx,y=exsiny. We have to find the critical point of fx,y. Differentiate…

Q: 7. Alan has 20 ducks and goats on his backyard. The animals have 64 legs altogether, how many ducks…

A: Alan has 20 ducks and goats on his backyard. Animals have 64 legs altogether. We have to find the…

Q: Q3/(a) Let d be a trivial metric on a set of X, find the induced topology on X by a metric d. (b)…

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Q: To find how much heat is required to bring a kettle of water to its boiling point, you are asked to…

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Q: 4. Solve the following 2nd order OPES (5 steps) day - (2x) + (1 - 1) dy dx² Y(0) = 4 h=0.02 ا = (

A: See below euler method

Q: 2. Write the equation x+ex = cos x as three different root finding problems g₁ (x), g₂(x) and g(x).…

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Q: 3. Integrate f 10(x+6) x² + 3x-10 2 dx by using partial fraction.

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Q: using Mathematica]

A: To prove that            ∫C-ydx+xdy=x1y2-x2y1 Where C is the line segment joining x1, y1 and x2, y2.

Q: old per ey as a ed an ins

A: This is a problem related to insurance calculation. Based on the policy of the insurance and concept…

Q: 3. Find a vector space basis for the following field field extensions: (a) Q(√2, √2) over Q. I

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Q: Equation: f(x) = 5cos(x) + sin(x) - 2sec(x) Tolerance: x10-5 Assume x = 0.5 (in radian)

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Q: Does the following series converge or diverge? 4√√n Σ 3/2 10n +7n+7 n=1

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Q: 7) A tumor is found with an initial mass of 3.5 grams. Its growth rate is measured and recorded in…

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Q: D. Suppose p, q, r, s are propositions such that p^q is true and rv sis false. Determine the truth…

A: We know that,  A∧B is true if and only if both A and B true  A∨B is false if and only if both A and…

Q: By direct partial integration, Solve the following PDES 8- X 8²Z 5 4 dz z(x,0) =X+X, Z (2,y) = 3 y z…

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Q: Q3: A Cummins diesel engine is available in heavy-duty pickup trucks. The probability of the engine…

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Q: 6 By separation of variables, Solve the following 5 PDES :- du dt = 2 d24 dx2 © o U (0₂t) =(4,t) U…

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Q: 3. Ronnie goes to the racetrack with his buddies on a weekly basis. One week he tripled his money,…

A: Let assume  $x he start with the first week One week he tripled his money = 3x But he lost $12 Left…

Q: 7) A can of soda with a temperature of 56 degrees Fahrenheit is placed in a refrigerator which is…

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Q: 2. Let f I→ R be Riemann integrable on I = [a, b], a, b = R, a <b, and let F be an an- tiderivative…

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Q: Using Parseval's theorem, establish 1 1 1 TL² 12+ 32 +52 + = ² 8' where Euler-Fourier coefficient of…

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