Compute the surface integral over the given oriented surface: F = y³i+8j-æk, ffs F. ds = portion of the plane x + y + z = 1 in the octant x, y, z>0, downward-pointing normal

Q: Find the area bounded by the curve and the line y = 13. Area = x = t-1/t y = t+1/t

A: We will find cartesian equation of the curve and identify the region bounded between curve and line…

Q: The volume of a gas in a container varies inversely as the pressure on the gas. If a gas has a…

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Q: 2. Why does the Implicit Function Theorem not show that the curve x² + y + sin(xy) 0 can be…

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Q: 3. Prove that A (B-C)=(AUB)(AUC); (a) with Venn Diagram, (b) with the pick-a-point method, (c) with…

A: Kindly refer to Step 2 for the solution.

Q: Find the critical points of the system below, and then use linearization to classify each one if…

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Q: aplace's Second Finite Integral for P, (x): P₁ (x) = -√5₁ de 72+1 [x ± √(x² - 1) cos 6] ¹+¹' nEN

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Q: Problem 5.38. Suppose f: X→ Y and let CCY and DCY. Prove: 5.38.1. f¹[CnD] = f[C] nf [D] 5.38.2.…

A: Given that, f: X→Y and let C⊆Y and D⊆Y. We have to prove that, 1. f-1C∩D=f-1C∩f-1D 2. f-1C\ D=f-1C\…

Q: and x" in a series of Hermite polynomials.

A: We have to  expand x^n in a  series of Hermite polynomial.

Q: Problem 1. For each of the following graphs G = (V, E), a. V = {a, b, c, d, e}, E = {[a, b], [a, c],…

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Q: Determine the natural boundary conditions at x = 0 and x = 1 for the func- tional I[u] = ¹ [(u')² -…

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Q: 2) X = {xx A^ (x B⇒ x # C) } is equal a) A' (B'UC') b) A'n (B'UC) c) Correct answer: A' (BUC') d) An…

A: Note: “Since you have posted multiple questions, we will provide the solution only to the first…

Q: Prove that Σ k=1 log k kp p> 1 converges.

A: The integral test says if ∫1∞fxdx converges then ∑k=1∞ak converges, where fx=ax. Now, given ∑k=1∞log…

Q: Classify the following as a linear relationship, exponential relationship, or neither. Explain your…

A: The regression is performed to fit a dataset into a function of the form: y=f(x). The linear…

Q: (a) Show that the series Σ₁²+1 n² + 1 n=1 converges using the Integral Test. Don't forget to state…

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Q: A company produces a spherical object of radius 22 centimeters. A hole of radius 4 centimeters is…

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Q: Let r > 0 be a positive real number. This problem will give a simple approach to limn→∞ rn. i.…

A: The given sequence is an = rn .  Our aim is to show that the recursive relation for the given…

Q: 3. Let f: R² R² where f(x, y) = (y³, x + y) and c = = (0, 1). 4. Let f: R² → R² where f(x, y) = (y³,…

A: (3)         f:R2 →R2         fx,y = y3 , x+y and  c=0,1 →1          fx,y = f1x,y , f2 x,y  f1x,y =…

Q: 1. Find the eigenvalues of A and then find a basis for the eigenspace associated with each…

A: Eigenvalue: A number λ is said to be an eigenvalue of a square matrix A if there exists a non-zero…

Q: The statement is either true or false. The statement is either true or false. If it is false,…

A: To Check: Whether the following statements are true or false: (a) Fora,b,c∈ℕ. at least a-b, a+c, and…

Q: Question 4. The Fourier series representation, FS(t), of a function f(t), where f(t + 8) = f(t) is…

A: The given problem is to find the values of Fourier coefficients an and bn  at n=1,2,3 for the given…

Q: Laplace's Second Finite Integral for P, (x): , (x) = = √5² T P₁ de [x ± √(x² - 1) cos 0]+1 * nEN

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Q: Match the third order linear equations with their fundamental solution sets. 1. y - y" -y + y = 0 2.…

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Q: Eliminate the parameter to find the cartesian equation of the curve: The equation of the curve is: x…

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Q: The figure F, shown below, is a square-based pyramid with edges all of equal length. The location of…

A: Given is a figure F, is a squared base pyramid with edges of all of equal length. The top vertex is…

Q: Use the method of undetermined coefficients to solve the nonhomogeneous linear system *-[1]+[+] X -t…

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Q: Use the quadratic formula to find the two roots. Here is the quadratic formula: -b + Vb^2- 4ac/2a…

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Q: 6. Derive the Brafman's generating Jun (c), H₂(x)" = (1-2xt)™ 2 Fo n! n=0 1/ ₁ / 0 + 1/ ; __ -…

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Q: Prove that x113+x-1≡0(mod 113) has no solutions in x.

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Q: Find a representation of the vector AB= (11, -15) in R2 by giving appropriate values for the points…

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Q: The graph below is of a function f(x) for some function f(x) with domain (-∞, =). 10 -5 (b) f(-8) =…

A: We know that the Integral represent nothing but the Area bounded by the curve f(x) above the…

Q: Which of these equations use incorrect mathematical notation for vectors? Tick all of those that…

A: We have to check which of these equations use incorrect mathematical notation for vectors . (A)…

Q: 5.3.8. Explain why the Frobenius matrix norm on Cnxn must satisfy the par- allelogram identity.

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Q: 6. Derive the Brafman's generalin ¯ (c)„ H₂ (x)¹″ = (1-2xt)˜° 2Fo Σ n=0 +] [i{^~~") -

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Q: dr (linear differential equation) Solve:- de +rsec 0 = cos 0.

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Q: Determine whether the equation +t + (cos²t)y = t³ is linear or nonlinear. Explain d³y dy dt3 dt why…

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Q: Solve the initial value problem below. x²y'' - 5xy' + 13y = 0, y(1) y = = — 4, y’(1) = - 14

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Q: Please advise. Keep on tossing a coin until one gets a head.  List 2 possible outcomes from this…

A: We can list two possible outcomes from this sample

Q: For the following systems, the origin is the equilibrium point. 3. a) Write each system in matrix…

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Q: Question 4. The Fourier series representation, FS(t), of a function f(t), where f(t + 8) = f(t) is…

A: Given that the Fourier series of f(t) with period 8 is…

Q: If (2 e)(1-3e-38) f(t) = C-¹ · L-₁ { (2²-0") (1 3e-1)} is continuous for t≥ 0, find f(1), f(2), and…

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Q: The lifting force, F. exerted on an airplane wing varies jointly as the area, A, of the wing's…

A: If x is directly proportional to y, then it can be written that x∝y or x=ky, where k is the constant…

Q: a. 0(x) = V b. w(x) = sin 0+2x-5 37+4 c. y(x) = mx-5 d. (x) = 5 cos(+3) 1. The model of linear…

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Q: Find the line integral of F = (3x2-5x) i+5zj+ k from (0,0,0) to (1,1,1) over each of the following…

A: we calculate the value of line integral using the general formula ∫F.dr.

Q: Write your answer in exact form and in terms of 7. Use an appropriate coordinate system to find the…

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Q: Use Stokes' Theorem to find the circulation of F = 3yi + 2zj + 2xk around the triangle obtained by…

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Q: Consider the parametric curve: x y Use a graphing device to graph the curve and check your work. =…

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Q: Initially a tank is filled up with 150 gallons of water in which 300 lb of salt is dissolved. Brine…

A: Initially the tank has 150 gallon of water. 300 lb of salt is dissolved. Brine with concentration 1…

Q: 0 ccab(ar) Dzah(x) || 2.000(x4/2)

A: The given problem is prove the following definite integral using method of complex variables.

Q: Define T:R2 R2 by T(x) = Ax. Find a basis B for R2 with the property that [T] is diagonal. A = 51 15…

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Q: Line integrals Use Green’s Theorem to evaluate the following line integral.Assume all curves are…

A: We know the Green's theorem, let C be positively oriented piecewise simple smooth closed curve. Let…