Calculate using polar coordinates. √4-7² 2 siste o x² + y² dy dx

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A: As per the guidelines I have solved first question.

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A: Geometric series Harmonic series Hypergeometric series Alternating series Multiplication series

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Q: b) y"+y=0.

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Q: 81-82. Looking ahead: Area from line integrals The area of a region R in the plane, whose boundary…

A: To Show: Area of the disk R=r,θ:0≤r≤a, 0≤θ≤2π using line integrals, A=-∫ydx is πa2.

Q: Determine whether the matrix is diagonalizable. Justify your answer. ? =    0 0           5 0

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A: We solve given series by Alternating series test (Leibnitz's test)

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Q: Answer the following questions about the function whose derivative is given below. a. What are the…

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A: Let us denote the integrand by fx=lnx. We have to compute the integral ∫13 lnxdx using the Simpson's…

Q: Q14. A red and a blue die are thrown. Both dice are fair. The events A and B are defined as follows:…

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Q: Prove that : L²₁ (1-x²) Pm Phd x T 0. 2n (n + 1) 2n + 1 4 mn. m = 11. m, ne N

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Q: The volume of the solid obtained by rotating the region enclosed by y = x², x = y² about the line x…

A: Introduction:   A solid of revolution is the result of rotating a section of a plane around a line…

Q: Use the simplex method to find the maximum value of the objective function, given the constraints…

A: Max P=21w+14x+20y+10z Subjected to constrain  12w+5x+2y≤303   w+x+y+z≤59…

Q: Prove that: L₁ (1-x²) PPdx 0, 2n(n+1) 2n +1 mn. m = 11. m, ne N

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Q: How many edges does a tree with 10,000 vertices have? Multiple Choice O 10,002 9998 10,001

A: We have to find the number of edges of a tree with 10,000 vertices.

Q: Let R be a relation on A = {1, 2, 3, 4}, such that: R1 = {(1,2), (3,4), (4,3), (2,1), (3,3)} R2=…

A: Since you have posted a question with multiple subparts, we will provide the solution only to the…

Q: au fferential equations and+p(x)v=g(x), dx espectively. If u(x₁) > v(x₁) for some x, and f(x) > g(x)…

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Q: Prove that: L'₁ (1-x²) Pm ³ dx = 0. 2n(n+1) 2n + 1 mn. m1 = 11. m, ne N

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Q: 1. Find the coordinate of the focus for the parabola 2x-y² +6y=1. Find the points of the latus…

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Q: [ 0 1 -2 1 ] , [ 3 1 -1 0], [ 2 1 5 1] find bases for the spans of the vectors in the given…

A: Given the vectors 01-21, 31-10, 2151. To find the bases for the spans of the given vectors. The…

Q: Let A and B be nonempty sets. Prove that A x B = B x A if and only if A = B.

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Q: (b) Use the alternating test to study the convergence of the series x 2" Σ(-1)" n! n=1 Remember to…

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Q: A hemi-spherical tank of radius 2 m is initially full of water and has an outlet of 12 cm²…

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Q: Consider the convergent alternating series If n = 4, then Sn = (-1)" = L. Let S₁, be the nth partial…

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Q: Evaluate ∞ fe-³x. erf (x) dx 0

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Q: First derivative of ₂ F₁(x): a.b d{2F₁ (a, b; c; x)} = ªb 2F₁ (a+1, 6+1;c+1;x) b dx

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Q: Q1. Solve the equation 110A 3sin²(x) = 4 cos(x) - 1 for 0<x< 360°, giving your answers in degrees to…

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Q: Find the value of X₁, X2 and X3 usin Method Gauss-Seidel and Gauss-Jacobi Provide the complete table…

A: Given: x1+2x2-x3=6x1-x2+2x3=-32x1-x2+x3=-1 To find: The values of x1, x2, x3 using Gauss-Seidel and…

Q: A triangle can be formed by drawing line segments on a map of Texas connecting the cities of Dallas,…

A: San Antonio to Houston 188 mi=3 in  So, distance from Dallas to Houston is 188*3.75/3 = 235 mi.

Q: Let R1 and R2 be two different relations on the same set A. If R1 - R2 is reflexive then R1 is…

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Q: Evaluate the integral I = fi di around the circle (x-2)² + (y - 3)² = 16, z = 0, where = (x² + y2²)i…

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Q: a) Using the first shift theorem, when necessary (see below for a statement) write down the Laplace…

A: (i) f1t=-5e-3t,   t≥0 We know Le-at=1s+a ∴Lf1t=L-5e-3t                  =-51s+3…

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Q: Solve the system of linear equations. (Enter your answers as a comma-separated list. If there is no…

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Q: a. Find the open interval(s) on which the function is increasing and decreasing. b. Identify the…

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A: The curve whose equations referred to rectangular axes are  x=3t,y=3t2,z=2t3 we have to prove that…

Q: M(x) = 7 (1.080)* (rounded $value) ✓ M(0) = ✓ M(10) = ✓ M(20) = ✓ M(40) = a. $15 b. $33 C. NA d. $7…

A: M(x)= 7(1.080)x

Q: Solve the game with the given payoff matrix. -1 1 2 2-1 0 P = 2 -1 -2 3 2 Optimal row player…

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Q: F(s): = S s²-10s+29

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Q: Compute the optimal rank-2 approximation of the symmetric matrix 5.00 0.50 -1.50 0.00 0.50 5.00 0.00…

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Q: Find the volumes of the solids Set up and evaluate an integral to find the volume of the…

A: Given That : A solid circular frustum of height h and radii a and b. To Find : Set up an integral to…

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Q: converges. Suppose an ≥ 0, and Σ an diverges. Show that an an +1 Prove that if an is a convergent…

A: We know that ∑n=1∞an is convergent if sequence of n-th partial sum of the series is convergent.…

Q: Find A. A = 24 -- [34] 2 (8A)-1

A: Inverse: A matrix B is said to be the inverse of the matrix A if AB=BA=I, where I is the identity…

Q: (For Economists). Per Mayvelin Caraballo of The Manila Times last September 20, 2021 digital…

A: Given that at the end of 5 years the balance in the account is given by the model as follows:…

Q: 1. How many "cups" of milk is needed? 4 1/2 2. How can you decide WHAT we to do? Let's draw it OUT…

A: 412 cups of milk is needed for the Michelle's moist cake recipe. Now we have to find how many times…

Q: Identify the isolated vertex from the given graph. Multiple Choice O O a d b

A: Vertex is where two or more edges meet. The degree of a vertex is the number of edges originating…

Q: Let A be the set of all permutations of the 26 letters in the English alphabet. The relation R on A…

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