1. Sketch the path C which is around the paths one from z = 3i to z = 2i and another from z = 2i to z = 2+i and hence evaluatef. (2z+3) dz.

Q: Let P denote the path that travels along the graph of y = x2 from (0,0) to (1,1). Let f(x,y) = √1 +…

A: Let P denote the path that travels along with the graph of y=x2 from (0, 0) to (1, 1). Let f(x,…

Q: Let F = Vf and f = 2zy + 8xy + 6xz. Calculate F. dr for the path r₁ = (t,t,t), 0 ≤ t ≤ 1. (Give your…

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Q: If A = x a, – zy a,, evaluate § A · dī around the path L defined by 0 < x < 2,0 < y < 1 as shown in…

A: Stroke's theorem:         It is also known as Generalized stroke's theorem. It states that the…

Q: S. 1.110. Determine whether A dr is independent of the path C joining any two points if (a) A =…

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Q: A 1-i

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Q: A) compute x the component of x that is parallel to L and x the component of x that is orthogonal to…

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Q: Let A = psino a,+p a,. Evaluate A dl given that L is the path shown in the figure. 1. Verify your…

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Q: Compute I ds over the path C : ř(t) = (t², 2t, t²) from (0,0,0) to (4, 4, 4).

A: Given path is:

Q: B H E RE OF G 3 A E D 2. Determine if each of the graphs above have a Hamiltonian circuit. Explain.

A: Remark: A path begins and ends on the same vertex (i.e., a closed circuit) such that each vertex is…

Q: Determine whether the work done along the path C is positive, negative, or zero. zero O negative O…

A: We know,       work = ∫cF.dr               = ∫c∥F∥∥dr∥ cosθ    where θ is angle between F and drIf…

Q: (G) G)- The projection of onto the line through zero 1 is and а. (;) () " () b. C. d.

A: Let u→=11, and the line l through zero v→=00, and w→=1-1. Need to find the projection of u→ onto the…

Q: 29. Calculate /| (xy +e*)ds, where S is the triangle in Figure 18 with vertices (0,0, 3), (1,0, 2),…

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Q: [2 Lo 2. and defined T: R² → R³,by T(X) = AX. Let A Find the images under T of u = |E|, and v =

A: Given a linear transformation T:R2→R3 by T(X)=AX where A= 2002

Q: Exercise 1.2.16 Find the circle x²+y² +ax+by+c=0 passing through the following points. а. (-2, 1),…

A: a) The given equation of the circle x2+y2+ax+by+c=0 Since the points (-2, 1), (5, 0) and (4, 1)…

Q: Evaluate fr z sin(z2) dz where I is the union of the directed line segment that joins the origin to…

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Q: Which of the following would be a line of reflection that would map ABCD onto itself? 3 B 2 D Ox=1…

A: For the solution follow the next steps.

Q: Show that 6.8) fdx + gdy = Jc.8) (12,16) • (12,16) - (28x³3 By³dx + 35ytx dy) is independent of…

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Q: 3.2 Evaluate where z = x + iy with y the path on line from z = 2+i to z = 1 + 2i.

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Q: Compute I ds over the path C : ř(t) = (t², 2t, t²) from (0, 0,0) to (1, 4, 4).

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Q: Determine whether the work done along the path C is positive, negative, or zero. y O positive…

A: Consider that the sign of the work depend on the orientation of the path C. here the circulation can…

Q: Construct a table that displays the number of directed paths of length 1 or 2 between each pair of…

A: Fill table by the number of directed path between two vertices . If the number of directed path…

Q: Suppose NOL -> QRM is a reflection across the x-axis. If O(9, 4) what is the y coordinate of R?

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Q: Let F(x, y) = (x, 0). Prove that if C is any path from (a, b) to (c, d), then F dr = 3 – a²)

A: Consider the provided information, Let Fx,y=x,0. Prove that if C is any path from a,b to c,d then…

Q: 3 4 Let y = -7 and u = -6 -4 1 Compute the distance d from y to the line through u and the origin. d…

A: The projection of a vector on a plane is its orthogonal projection on that plane. In simple words,…

Q: 4 3 Compute o dzwhere C is the circle 2- i = 2 traversed once z+2i (2- 2i), C. counterclockwise…

A: By cauchy integral formula we can solved the problem

Q: Show that Sa fdx + gdy = Sa - (16x*y²dx + 8yxʻdy) is independent of path: (10,5) –2) (10,5) ,-2) 4…

A: We are given a line integral as follows : ∫1, -210, 5 fdx+gdy=∫1, -210, 5 -(16x3y2dx+8yx4dy)   First…

Q: P(5,3) Sinh (폼+북) x +1oydy (6xdx +10ydy 5 C0,0)

A: To show: The line integral is independent of the path. Given integral:…

Q: Calculate / Ss (4xy + e- )dS, where S is the triangle in Figure 1 with vertices (0, 0, 3), (1,0, 2)…

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Q: 1. If 4 = xy i+yzj+zxk, find curl4 and curl curl A at points (1,2, –3).

A: Given that A = xy i + yzj + zxk and find curlA and curlcurlA at point (1,2,-3). Here i attached…

Q: 26. Let F(x, y) = (3x + y, a?y) and let C be the path along ry = 2 from (1, 2) to (2, 1). Calculate…

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Q: Determine whether the work done along the path C is positive, negative, or zero. y

A: The work done along the path C is

Q: (a) Solve the following Goursat problem for u(x,t): Utt = Uxx +4cos 2t, (t > 0, -t <x<t), u(t,t)…

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Q: Determine whether the work done along the path C is positive, negative, or zero. c/

A: we know that Work W=∫C F→·dr→

Q: Evaluate I = ,(sin x + 2y) dx + (5x + y) dy for the nonclosed path ABCD in the figure. C A = (0,0),…

A: We will split the total integral into three paths I.e. along AB,BC,CD  Then we will evalute three…

Q: Consider the path r(t) (14t, 7t, 7 In t) defined for t > 0. Find the length of the curve between the…

A: Given - r(t) = ( 14t, 7t2, 7lnt )  defined for t&gt;0 To find - The length of the curve between the…

Q: Determine whether the work done along the path C is positive, negative, or zero. Ozero negative…

A: To determine whether the work done along the path C is positive , negative or zero .

Q: -6 3 Let y = -5 and u = -4 -2 Compute the distance d from 3y to the line through u and the origin.

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Q: -4 -8 Let y = 9 and u = -2 -8 7 Compute the distance d from y to the line through u and the origin.…

A: I have appended the formula used in the solution part of the question

Q: 2. 22 – x2 1 By sketching the traces on the ry-, rz- and yz-plane a.

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Q: 4. let f(x, y) = x² – xy + y² – y. find the direction u and Duf at Po(1,–1) for which Duf is the…

A: Given:- f(x, y) = x2 -xy+y2 -y To find:- Direction u and Du f at point p0 (1, -1) for which Du f is…

Q: Evaluate I = Se(sin æ + 7y) dæ + (3x + y) dy for the nonclosed path ABCD in the figure. А 3 (0,0),…

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Q: Evaluate zdz from z=0 to z-4+3i along the curve C given by the line from z=0 to z=3i and then the…

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Q: Determine whether the work done along the path C is positive, negative, or zero. /c/ zero negative…

A: For calculating the work done from the field we will have to see the direction of both vector field…

Q: 8 -2 Let y = and u = 1 -6 Compute the distance d from y to the line through u and the origin. d =

A: Solution:

Q: Determine whether the work done along the path C is positive, negative, or zero. negative positive…

A: Consider the provided graph, Determine whether the work is done along the path c is positive…

Q: Consider the path r(t) = (4t, 2t², 2 In t) defined for t > 0. Find the length of the curve between…

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Q: 3.1 Show that upper bound of fe dz, where C is the circle |z + 4 – il = 7. z+5i-1

A: The given problem is to find the upper bound of the given complex integral over the region of circle

Q: Suppose NOL -> QRM is a reflection across the x-axis. If O(1, 9) what is the y coordinate of R?

A: