Let F = (yey, xey) and let C be given by: x = sin(t), y et-¹ (1- = cos(πt)), 0≤ t ≤ 1. Show that is conservative and find a potential function f. Evaluate F. dr using Theorem 2.

Q: 2. Prove that the union of two disjoint sets, where one is countably infinite and the other is…

A:

Q: Using n = 2 equal-width subintervals, approximate the area of the region bounded by the graph 3 of…

A:

Q: Consider the following matrix A and its reduced row-echelon form: -2 6-2 2 -10 -10 -6 18 -4 4-24 -22…

A:

Q: Use Definition 7.1.1, DEFINITION 7.1.1 Laplace Transform Let f be a function defined for t≥ 0. Then…

A:

Q: 3. Let R. be a commutative ring with ideals L and M. Give an example of when LMLn M.

A:

Q: Find the line integrals of F = 2yi + 3xj + zk from (0,0,0) to (1,1,1) over each of the following…

A: Note: We will be solving part (c) for both functions as asked.(1)The given vector valued function is…

Q: Find the center of mass of a thin plate of constant density 8 covering the given region. The region…

A: Given region is bounded by Let  be the centre of mass of the given region.then we have the following…

Q: Let A = [3 -3 0 14 20 1 We want to determine if the columns of A span R². To check this we add times…

A:

Q: 7. 8. Another way of writing 5 = log41024 is a) 54 = 1024 Evaluate log525². a) 25 b) 1024 = 45 b) 4…

A: logbx = y is equivalent to by = x ,where x > 0 ,y > 0 ,b > 0 ,b ≠ 1.logaa = 1 for a>…

Q: A calculator is required for the following questions. Questions 12-14 refer to the following…

A: Given that the velocity of a particle moving along a line given by

Q: Please answer True or False for the following Statements... 1. For every odd integer n, the integer…

A:

Q: sinx x0e²x -1° 5. Use power series to evaluate lim

A:

Q: Select the letter of the correct response. Investigate the series n=1 (a) Converges by Root Test…

A:

Q: Uy = Clzzi on the domaion 0≤x≤ 2, t > 0, subject to u(x,0) = x(x − 2), u(0, t) = 0, u(2, t) = 0.

A:

Q: 2. Solve the following first-order differential equation. dy dx 4 (5 + x) y Initial condition y(0) =…

A:

Q: Given f(x)=(2x^2-2)/(x^2+2x-3) Write the domain of f in interval notation Simplify the rational…

A:

Q: [3 0 -9 -25 -33 We want to determine if the columns of A span R². Let A = To check this we add times…

A:

Q: We say that a set A is denumerable if there exists a bijective function f : N→ A. Suppose that A and…

A:

Q: Show that A = P-¹ = 2 -1 -5 2 -2 -2 0 1 -4 and B = 3 6 -8 2 2 -4 , P = 4 6 are similar matrices by…

A: Given: and To show: and  are similar matrices by finding an invertible matrix  satisfying

Q: (a) Find the Fourier series of the function f(x) = x²,0 ≤ x < L with period L. In the following,…

A: Given function f(x)=x2 defined in [0,L] with period L.The Fourier series is of the…

Q: The formula used to measure sound is L = 10log (), where L is the loudness measured in decibels, I…

A:

Q: Find the infimums of the sets S={1/n : n∈ ℕ+} and T={ (-1)n/n : n∈ ℕ+}. Is either infimum a minimum.…

A:

Q: For the following function, you are given one period of the function. f(x) = sin tx on the interval…

A: The given function is  on the interval .We need to draw several periods of the function.Expand it in…

Q: - Evaluate S using upper and lower sums. HINT: x³ dx b4-a² = (b³ + b²a+ba² + a³)(b − a).

A: Using the Upper Riemann sum and the lower Riemann sum we shall solve this problem .

Q: When solving the Sturm-Liouville boundary value problem y" - Ay=0, 0<x<L, subject to the y'(0) = 0,…

A:

Q: In how many ways can we seat 6 boys and 3 girls on a row of seats so that no two girls sit next to…

A: If no two girls can sit together, then we need to alternate boy and girl. We can start with a boy…

Q: Consider the following function. f(x) = sec(x), a=0, n=2, -0.4 ≤x≤0.4 (a) Approximate f by a Taylor…

A:

Q: 41. Evaluate the line integral over the given curve C. (9x + 3y)ds; r(t) = (t - 9)i + tj, 0 ≤ t ≤ 4.…

A: We have to evaluate the line integral over the given curve C."Since you have posted multiple…

Q: A standard card deck has 52 cards. How many thirteen-card hands are standard deck? possible from a

A: The objective of this question is to find out the number of possible thirteen-card hands from a…

Q: Problem Set C 19 Given: AKOR is equilateral. KOPR is a . KMOR is a 0. Prove: AJMP is equilateral.…

A: 1) In a parallelogram, opposite angles are equal.2) In triangle, the sum of all three angles = 180…

Q: Find fourier series for the periodic function given by : f(t)= |2t| 0≤t ≤1

A:

Q: 14. In a right triangle, a line perpendicular to the hypotenuse drawn from the midpoint of one of…

A:

Q: You need to pay attentien on this one. I want you to find the interval of convergence for the…

A:

Q: Solve the system of differential equations x₁= 2x1 + 0x2 x2 = −7x1 + 5x2 x₁(0) = 2, x₂(0) = 0 x₁(t)…

A:

Q: √ . Evaluate I /16-2 √x² + y²dydx using polar coordinates.

A:

Q: Let a₁ = [+] and b = 12 [23] 28 Is b in the span of of a₁? A. Yes, b is in the span. B. No, b is not…

A:

Q: At a certain company, passwords must be from 4-6 symbols long and composed from the 26 uppercase…

A:

Q: Rewrite the triple integral rb pg2(=) Lot fore) als f(x, y, 2)dædydz a g₁(:) h₁(y,:) ffff(x, y, z)…

A:

Q: Factor f(x)=x^5-3x^4-6x^3+26x^2-27x+9, given that 1 is a zero of multiplicity 3.

A:

Q: Consider the Boundary-Initial Value problem 8² u du 0 0 მx2 Ət u(0, t) = 0, u(8,t) = 0, t>0 u(x, 0)…

A:

Q: The number of different mammal species observed along a transect through a forest is a random…

A: The probability mass function for the random variable X is given by                 |–   0.01…

Q: 4. Let A be a square complex matrix with invariant factors 1, A(A — 2), A³ (A — 2) Answer the…

A: Since you have posted a multi subparts question according to guidelines I will solve first three…

Q: (2) Suppose ƒ is continuous on [a, b] with f(x) ≥ 0 for all x € [a,b]. If | f(x) dx = 0, show that…

A:

Q: Let a and BE R. Consider the linear optimization model: min s.t. x1 + x2 αX1 + βα2 > 1 x1 ≥ 0,₂ € R.…

A: Let .Consider the linear optimization model (Pα,β)..Subject to:We need to write the linear…

Q: Let S denote the surface of the box [-2,3] x [-4,2] × [0,3], ori- ented outward, minus the disc that…

A: Given that the surface S denotes the box [−2,3]×[−4,2]×[0,3].The orientation is outward and the…

Q: Assume S is the surface x1000+y8000+z1000 = 10¹2 and f = (9+ eyz, x³yz, 3x - 5y - 6 cos(zx)).…

A: Here we use the Divergence theorem for a surface S inclosing a volume V

Q: Problem #3: Let Problem #3: A = B 6 Find a unit vector x whose first component is positive at which…

A:

Q: Find the integral if the region is given by | z+1-i 1 - 5z + 6 z²- z³2z - 4

A:

Q: Let S₁ and S₂ be the surface whose the equation in spherical coordinates are given by: $₁:$=1/53₁ -…

A: Given information:For ​For To find:Rectangular coordinates representation of and .Volume of the…

Q: 1. Classify the (0,0) equilibrium of each of the following 2x2 sys- tems by type and stability: [2…

A: