Consider the vector field F(x, y, z)=-yzi + (xz+y²)j +e³k, and let C be the curve illustrated below consisting of the boundary of the triangular region with vertices at the points (1,1,2). (1,0.2) and (0,1,2) oriented counterclockwise when viewed from above. Compute the line integral fF.dr using either a direct computation, or using Stokes' theorem. Note that one of these two methods will yield a much simpler computation than the other one, so choose the method carefully. (1,0.2) (0,1,2) ť

Q: nº as a polynomial { The numbers S(p, k) are called the Stirling numbers of the second kind. Find…

A: The polynomial p has degrees less or equal to n and I'm trying to prove sum k = 0 to n…

Q: Let X= {A ⊆ ℝ| 1 is not in A and ℝ \ A is finite}. Prove that ℝ is a compact Hausdorff space with…

A:

Q: Question 10 Use Gaussian Quadrature of order 5 to approximate 2 6 4 x-1 To how many decimal places…

A:

Q: Express the system of differential equations in matrix notation. x' = 3x +9y y' = 4x-9y Write the…

A:

Q: FORMULA FROM EXPONENTIAL GRAPH The figure shows the graph of an exponential function. The dots on…

A:

Q: Problem #7: Consider the differential equation 2x²y" + (x² + x)y' - y = 0. (a) Without solving this…

A:

Q: Find all solutions to the equation below in the interval [0, 2π). Give all answers as decimals…

A:

Q: Given the functions f(x) = x² + 3x + 2 and g(x) = x + 1, determine a simplified equation for h(x) =…

A: Solution :   Given that the functions   f(x)=x2+3x+2 g(x)=x+1

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

A:

Q: 01: An important concern in the study of heat transfer is to determine the steady-state temperature…

A:

Q: -2πT Compute fo 1 1+cos² @de.

A:

Q: A group of 1200 incoming first year students was interviewed to tell which modality they prefer to…

A: let  A=students who prefer full-online modality B=students who prefer blended learning modality…

Q: Find the Wronskian for {x2, ex^2, x2ex

A:

Q: 3x -y - 2z = 1 -x + 6y -3z = 0 -2x-3y + 6z = 6

A:

Q: 2-1 7 s² +49 2

A:

Q: Use double integration to evaluate the volume of the indicate solid. 4 3 27 11 y=x z=4-x-y y = 2

A: Volume of a solid region E bounded above by z=f(x,y)  V=∫∫Df(x,y) dx dy  Where D is the projection…

Q: Graph the function f(x) = u₂(x) ln x + u5(x) (ln(10 − x) – In x) -

A:

Q: Determine whether the series converges or diverges. Σ=1n(3-2 Inn) Note: a P = 1 ар Select the…

A:

Q: (a) Find the equation of the tangent line to the curve y = x² at x = 1. (b) The line in part (a) is…

A: Sol:- Find the tangent pointPlug x=1 into the equation fx=x2 tangent point = 1, 1Find the slope of…

Q: sin(2x) Computedx.

A:

Q: In theory, the partial sums of this series could be used to approximate 7. a. Show that the series…

A:

Q: Consider the following. Initial Condition (0, 23) (a) Use Euler's Method with a step size of h = 0.1…

A:

Q: 5. Construct the state diagram of the following overlapping sequences. a.) 10110 sequence using…

A: "Since you have posted a question with multiple sub-parts, we will solve first three sub-parts for…

Q: 10. f(x)= x + x −1

A: Newton Raphson Method: Let f(x) be a differentiable function. To find the root of the equation…

Q: In Romberg integration, R42 is of order: 02

A: “Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: 5. ) Let l: R₂[x] →→→R³ be a linear transformation such that l(1) = l(x) and l(x²)=1 (a) Find a…

A:

Q: Question 3 Consider the system x' = x+y+4e²t y = 3x - y (a) For the associated homogeneous system,…

A: Given non-homogeneous system is x'=x+y+4e2xy'=3x-y its associated homogeneous system is…

Q: I VOLUMES OF REVOLUTION 1. Find the volume generated by revolving about x-1, the area bounded by y =…

A: ABC part is the closed region by the curve and x-axis.

Q: Consider the system x' = x+y+3e¹t y = 15x - y (a) For the associated homogeneous system, calculate…

A: Given : x'=x+y+3e4ty' =15x -y To find :(a)  determine its stability             (b) general solution…

Q: Calculate the double integral where R = [1,2] × [-1,1]: R xeᎩ dᎪ

A: Sol:- It can be re-written as :- ∫12∫-11xeydydx......................(1)First siolve this…

Q: Show that for any x, y E R2 we have doo (x,y) ≤ d₂(x, y) ≤ d₁(x, y). Under what conditions on x and…

A: We have to show that for any (x, y)∈ℝ2 ,  d∞(x, y)≤d2(x, y)≤d1(x, y) And under what conditions,…

Q: Let D be the region enclosed by the two paraboloids z = 2x² + y² and z = 9-x²-8y2. Then the…

A: We need to determine the projection of the region bounded by the curves: z=2x2+y2 and z=9-x2-8y2 on…

Q: What does the 400 Blows teach filmmakers that they should do about their films and filmmakers

A: The 400 Blows directed by Francois Truffaut is an iconic film of the late 1950s that refined French…

Q: A project has 75 activities but we have only a partial information as shown below: m activity H,…

A: Clear explanation is given below

Q: This question examines your understanding of the rank of a matrix. Please tick all correct…

A:

Q: 5. If  Z ~ N(0,1) with  P(Z < a) = 0.7 and P(Z < b) = 0.8122. a. Find P(a <Z < b) b. Find the…

A:

Q: Let T: P₂ → R² be the linear transformation. Given that M = (1,x+x²,2-3x2) and N = {(₁).(2)} are…

A: Linear transformation

Q: For each of the following explain the transformation from y = cos(T): a) y = cos 2(T) b) y = 3 cos…

A:

Q: Let D be the region in the first octant enclosed by the two spheres x² + y² + z² = 9 and x² + y² +…

A:

Q: Write the equation of the new parabola in vertex form y = a (x - h)² + k. If there is no value for…

A: Introduction: The technique of altering an existing graph or graphed equation to create a different…

Q: 13. List the Taylor series centered at x=0 (that is, the Macluarin series) for each of the following…

A:

Q: Let Find an orthonormal basis of the row space of A. A = 1 4 1.[C ]]}.

A:

Q: Problem #2: Consider the following differential equation. (1 + 5x²) y" - 9xy' - 3y = 0 (a) If you…

A:

Q: 10. ∞ Show that the series converges: Σ n=1 a. Find the 25th partial sum: S25 · (−1)n+1 2η2 +1

A:

Q: Express the system of differential equations in matrix notation. x' = (e ¹)x+ (at + bt³)y y' = (tan…

A: The given system of equations is ,           x' = (et)x + (at+bt3)y             y' = (tan t)x + (…

Q: b. The FIFA World Cup 2018 in Russia consists of 32 teams. How many ways for the top 3 teams exist?

A:

Q: Use cylindrical shells to find the volume of the solid obtained by rotating the region bounded on…

A: Solution:-

Q: (a) Over what interval(s) taken between 0 and 2, noninclusive, is the graph of y= cos.x increasing?…

A: Increasing function: For a function y=fx, if the value of y is increasing, when the value of x is…

Q: Use the Laplace transform to solve the following initial value problem: x' = 12x + 4y, y -8x + e¹t…

A:

Q: Obtain the general solution to the equation. dy y dx X + 9x + 7 The general solution is y(x)=,…

A: