Construct a idempotent of order 3, L3. Find L4 latin square of order 4, L4, and a commutative latin square L3.

Q: 19. Σn!(2x - 1)" n=1

A: Let the power series be .To Find:a) Radius of convergence.b) Interval of convergence.

Q: (B) Calculate the double integral dR y+4x where R is the area which is bounded by the curves y = 4x,…

A: A double integral  where R is the area bounded by the curves .To Find: Evaluate the above integral.

Q: Consider the following functions. F(x, y, z) xi - zj + yk r(t) = 4ti + 9tj - t²k 16² F. dr, where C…

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Q: 4. (a) Test the series n=1 for convergence and divergence. (-1)^ (1+x)" 2n n² Hence, deduce that +…

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Q: Сав (аль) =ажь b = ⇒ inverse of (a*b) = axb. (ахь) = ажь) П

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Q: Let u = (−3, 2), v = (3, −2) and A = - [ i]. 1 4 NOTE: Give exact answers. | (a) Find ||u|| relative…

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Q: (B) If f(x,t) = fakt e-y²dy, then prove that kfx = ft.

A: (.)  Leibniz rule :  Given

Q: Use the product rule to simplify. 2-5.26.5-7.56 2-5.26.5-7.56 = 2 5

A: Simplify the given expression .We have to factor the expression

Q: The median size of a new single family house built in the United States between 1987 and 2001 can be…

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Q: Consider the following system. λ = dy dt 2 Find the eigenvalues of the coefficient matrix A(t).…

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Q: Find the maximum value M of ƒ(x, y) = x³ yª for x ≥ 0, y ≥ 0 on the line x + y = 1. Use symbolic…

A: To get critical points put first derivative equals to zero.

Q: Calculate fff (x, y, z) dS, where S is the part of the plane x + y + z = 2, where x, y, z ≥ 0, and f…

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Q: 7. Show that 8 s cos(ax) x4 +1 dx = π a a/√2 e-2/² (cos+ sin) COS √2 √2 a> 0.

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Q: Evaluate the integral ₁x²x² dz dy dx by converting to an equivalent integral in cylindrical…

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Q: II Basic properties of an inner product . Let V be an inner product space. Prove that the…

A: We have to prove that a norm is induced by an inner product if and only if, for all the norm…

Q: Suppose that a large mixing tank initially holds 500 gallons of water in which 50 pounds of salt…

A: Thus, we need to find  and  first.Here,         (concentration of salt in inflow).(input rate of…

Q: 4. Classify the following operators on R4 by similarity (missing entries are 0): (b) 200 2 (c) 0 NEN…

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Q: Find the Hermite equations given the starting point (1,3,1) and ending point (2,5,0). The derivative…

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Q: 1. Write the vector v = 3 as a linear combination of the vectors:

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Q: Metrics. Show that, for fixed x0 in E, the function  from E into ℝ+ is uniformly continuous.

A: Given:Let  be a metric space, and let ​ be a fixed element in .Objective:We want to show that the…

Q: 27. 28. In the following exercises, compute the Taylor or Maclauren series of each function around…

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

Q: Find the flux of the vector field F = xi + e³xj + zk through the surface S given by that portion of…

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Q: Show that a normed vector space is finite dimensional if and only if its closed unit ball is…

A: A normed vector space is a vector space over the real or complex numbers, together with a function…

Q: 1. Generate a vector field and insert a screen shot: a) F=

A: Vector field: .We have to insert a sketch of vector field.

Q: Q3. Determine whether the following series converges absolutely, converges condi- tionally, or…

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Q: Solve the system of differential equations. [6 -2] [2 13] T 2 10 x'= x₁ (0) = 14, x₂(0) = 26 X T₁(t)…

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Q: Use the Divergence Theorem to compute the flux of F across the surface of the solid S: F(x, y, z) =…

A: The vector field is  and S is the solid bounded by .To Find:Using the divergence theorem compute the…

Q: - (-1,2,1) 5. (3,1,1) yo (5,3,4) 18.mp (201²) ( 165/

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Q: Suppose that λ =A₁, A₂ are constants such that u(z,y) = F (z+ Ay) statisfied the PDE 82 -4 ( 5²2 U…

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Q: Five thousand tickets are sold at $1 each for a charity raffle.  Tickets are to be drawn at random…

A: To calculate the expected value (E(X)) of the raffle if you buy one ticket, we need to find the sum…

Q: 11. Identify R+¹ with the set Pn of polynomials of degree ≤n, via the corre- spondence (An, . . . ,…

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Q: could you write down in paper cause maybe its easier for me

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Q: Express the solutions of the given homogeneous system as a linear combination of basic solutions. -…

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Q: (i) Let F be a smooth vector field on a closed and bounded region D in R³. Suppose, the boundary of…

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Q: Find the point on the line y=2x+1 that is closest to the point (5,2)

A: The given problem is to find the point on the line that is closest to the point (5,2).Given line…

Q: Solve a) 7x=4 (mod 19), b) 4x=2 (mod 12), and c) 3x=9 (mod 12). I know that for a) x=4 and c) x=9…

A: We have the following equations:a) 7x=4 (mod 19)b) 4x=2 (mod 12)c) 3x=9 (mod 12)To Find:Solve the…

Q: 9 practice problem Evaluate the surface integral 2m F(x, y, z) = -xi-yj + z³k, S is the part of the…

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Q: How do you know whether it is associative and has an identity

A: Here, we have to check for associativity and identity element.

Q: Use Stokes's Theorem to evaluate [F F. dr. C is oriented counterclockwise as viewed from above.…

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Q: Find the inclination of the tangent to the curve y = 7x³ + 7x² + 18 at x = 17 in radians.

A: We need to know the slope of the tangent at x = 17 in order to calculate the inclination of the…

Q: A shipment of 30 inexpensive digital watches,  including 8 that are defective,  is sent to a…

A: Probability is a measure of the likelihood that an event will occur. It is expressed as a value…

Q: Find an LU factorization of the following matrix (with Lunit lower triangular). [-5 0 4 2 -5 10 A =…

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Q: How do you do the LCM?

A: The least common multiple of two integers a and b is denoted as lcm(a, b).In general the least…

Q: 3. Sexyds C is the unit circle r(t)= for 0 ≤ t≤2π

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Q: Prove the ultrametric triangle inequality |x + y₂ ≤ max{x\, \y\,}. Remark. Since max{\x|₁, \y\,} <…

A: To prove the ultrametric triangle inequality, will start with the definition of the p-adic absolute…

Q: The table gives the approximate height at quarter-meter intervals of a mound of gravel. Estimate the…

A: The solution is given by

Q: 4. The goal of this exercise is to prove the converse to Mashke's theorem in the special case of a…

A: The given information for the exercise is as follows: is a prime number. is a field of…

Q: 6. Prove the following Polarization Identity for an inner product space. That is, prove the…

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Q: Find the projection matrix for the column space of the following matrix 10 11 11 10

A: Solution: Given matrix: we have to find the projection matrix for the column space of the given…

Q: Construct a truth table for the statement below, then select the answer that matches your answer…

A: The given statement is .The objective is to construct the truth table for the given statement.