Evaluate | (3z2 – 22) dz, where C is parametrized by z(t) = t+iť, 0

Q: If a particle moves in the xy-plane so that at time t > 0 its position vector is (In (t2 + 2t) ,…

A: As we know that the expression for the velocity is; v=dstdt Given position vector is:…

Q: a. Find a parametrization of the curve x = (y* – 3)e2y.

A: We’ll answer the first question since the exact one wasn’t specified. Please submit a new question…

Q: 8.Evaluate the triple Integral. Te by The paraboloid X=2yt + 2z? and the plane X=2. 7x dV, where E…

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Q: In Exercises 39–42, find a parametrization c(t) of the curve satisfying the given condition. 40.…

A: Given: y=3x+4c(3)=(2,2)c(t)=?

Q: Express the given parametrization in the form y f(x) by eliminating the parameter. - In(t), y = 5 +…

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Q: Exercise (2): Calculate S. xydx + 3y*dy where C is the curve in xy plane, x = y² from (0,0). to…

A: We have to find the line integral

Q: In Exercises 31-36, find a parametrization of the tangent line at the point indicated. t,4t 2,2t 3),…

A: Differentiation: The line must pass through the point at t=-2 is  (t,4t+2,2t+3)=(-2,-6,-1)

Q: Let C be the line segment from [1 – i,2+ 2i). (a) Parametrize C. (b) Integrate 2 over C.

A: According to the given information, Let C be the line segments from [1-I,2+2i]. For part (b) it is…

Q: 9. An object moving along a curve in the xy-plane has position (x(t),y(t)) at dy dx :=1+ tan(r²) and…

A: According to Bartleby q&a guidelines I will attempt only one question

Q: Integrate counterclockwise dz by Cauchy's formula z2 – 16 counterclockwise around the circle C : |z…

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Q: 6: Find the work done by the force F = -7y i+ 10x j along one loop of the curver = sin 70 (in the…

A: Given

Q: find a parametrization c(t) of the curve satisfying the given condition.  y = x 2, c(0) = (3, 9)

A: The given function is y=x2 and c(0) =(3,9) Let x(0) =3 and y(0)= 9 Take x =t +x(0) Thus, x = t+3

Q: An elastic string is stretched between two points 40 cm apart. Its center point is displaced 1.5 cm…

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Q: 30. (2x + y²) dx + (2xy + 3y) dy C C: Any simple closed curve in the plane for which Green's Theo-…

A: We know that Green's theorem

Q: Evaluate the line integral f. (2x – 4xy)dx + 3xy – 2x³y)dy over the straight path L joining point…

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Q: Q2/ find the parametic equation for the line passi through the pont (o,1,2) that is parallel to the…

A: To find parametric equation

Q: Evaluate the line integral/ (ax + 2y)dx +x dy, where C consists of the path C from (0,0) to (3,0),…

A: Consider the provided question, Hello. Since your question has multiple sub-parts, we will solve…

Q: 1. Evaluate (32²-2z) dz, where C' is parametrized by z(t) = t+it², 0<t<1. 2. Evaluate (1 + iy) dz.…

A: Consider the line integral ∫C3z2-2zdz in complex plane, here the curve C is parameterized by…

Q: 3. If C is the unit circle in the complex plane C, and f(2)= =², show that f(z) dz = 0 using two…

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Q: 15. What is the correct piecewise parametrization of a path C created by starting from C₁ of…

A: Introduction: The parametrization is a very significant part that is related to vector calculus.…

Q: Evaluate fc F • dr, where F = (z, y2, x) and C is parametrized (in the positive direction) by r(t) =…

A: F=z,y2,x and C is the parametrized by r(t)=t+1,et,t2 for 0&lt;t&lt;2. We have to evaluate ∫CF·dr.

Q: Show that y^3dx+3xy^2dy=0 is separable and exact

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Q: In Exercises 31-36, find a parametrization of the tangent line at the point indicated. ( 1 - t 2 , 5…

A: Given: The line given is r(t)=1-t2,5t,2t3. Substitute 2 for t in r(t)=1-t2,5t,2t3.…

Q: Sketch the direction field of the D.E. y = y - t and the solution curves corresponding to y(0) =-1,…

A: Solution of question is written in below steps.

Q: Find a parametrization c(t) of the line y = 5 − 2x such thatc(0) = (2, 1).

A: This question comes under the category of calculus and from the parametrization of the line here we…

Q: Let z(a, y) = 7x – 6y where x = - 7s – 4t & y = – 2s + 8t. %3D %3D az Calculate as az by first…

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Q: Find a parametrization for the ray (half line) with initial point (3,2) when t = 0 and (- 1, - 1)…

A: Given points on ray is (3,2) for t=0 and (-1,-1) for t=1the parameterization isr(t) = u+tvwhere,…

Q: find a parametrization c(t) of the curve satisfying the given condition.  y = 3x − 4, c(3) = (2, 2)

A: To find the parametrization

Q: Express the given parametrization in the form y = f(x) by eliminating the parameter. x = 5t + 2, y =…

A: Given

Q: Exercise 1.3.2 Give a paramatrization for the curve curve y = x³ + ()x-¹, then deduce the length of…

A: Given curve is  y=16x3+12x-1

Q: 3. A particle moves in the xy-plane so that at any time t, its coordinates are given by x = t° -1…

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Q: 15. What is the correct piecewise parametrization of a path C created by starting from C₁ of…

A: Given Path C is C1:  y=x+3,     0≤x≤4C2:  y=x2,         y=7 to y=0C3:  line connecting C1 and C2…

Q: find a parametrization c(t) of the curve satisfying the given condition. y = x2, c(0) = (3, 9)

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Q: Compute the directional derivative of f(r. y) = = at the point (1, 1) in a irection normmal to the…

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Q: Evaluate (2z – z) dz, where C is parametrized by x = -t, y = t² + 2, 0<t< 2.

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Q: of the b) nd y- Fons c) with point.

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Q: 1. Show that the problem may be formulated in terms of the velocity potential (r, 0) satisfying r dr…

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Q: (a) Calculate the line integral (4x+2y²)dy where C' is the curve y = 2³, starting from z = 0, y = 0,…

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Q: 4y The divergence of the vector G = i+ sin y j+ 3k is :- -8y + cosy x3 الخيار 2 O

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Q: Suppose that C is the graph of a smooth vector-valued function r(s) parametrized by arc length with…

A: Introduction: The tangent vector to a vector valued function rt is formulated by the equation r't…

Q: In Exercises 31-36, find a parametrization of the tangent line at the point indicated. (lns)i + s- 1…

A: Given,    r(s)=(ln s)i + (s-1)j + (9s)k   at s = 1 Therefore,          r(s)=(ln s, s-1, 9s)⇒…

Q: 11 Calculate the line integral f Gy)ds for the given junc rion and path xiyl=xy KHt)=<3+,2t=-37 for

A: r(t)=&lt;3t,2t-3&gt;=&lt;0,-3&gt;+t&lt;3,2&gt; x(t)=3t  and y(t)=2t-3 ds=32+22dt=13dt 0≤t≤1

Q: 2. Compute the vector line integral: -y х — 4 Le (x – 4)² + y² dx + (x – 4)2 + y² dy where C is the…

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Q: Evaluate the path integral between the points A = (1,3) and B = (2,5) of: B *(x²y + 2y)dy, with y =…

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Q: What is the correct piecewise parametrization of a path C created by starting from C₁ of equation y…

A: Concept: We have given the curves  y=x+3x=0 to x=4y=x2 Here the red line represents y=x+3 The green…

Q: if f(x,y) =x2y÷x+y and y(t)=  (x(t),y(t)) is parametrized curve in domain of f with y(0)=(2,-1) and…

A: The first step in solving the problem is to obtain the parametric equation. The initial values can…

Q: Find the natural parametrization of r(t) = 1²0₂ + 20y. What is this curve?

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Q: find the general solution of the dipperential ation given below. y+ 2xy -xe-r?

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Q: 4. f(z) = { |z|* z = 0 verify that the Cauchy-Riemann equations are satisfied at the origin z =(0,0)…

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