Consider the oriented curve C given by as shown in the following figure: An expression that calculates the value of A) [[ 6ry dy dr 32² dyc 25 23 V off dz 3r² dy dr D) ») - [² [³³ C=C₁UC₂, where 3ry dy dr C₂ C₁: y = r³, C₁ I √3³ dr + (2³ + 3xy²) dy and C₂: y = r. corresponds to:

Q: 3) Consider the curve C in R³ given by: r(t) = (t + In t, t – In t, 4t'/²) con 1<t< 2 An expression…

A: Formula: If r(t)=x(t), y(t), z(t), a≤t≤b is parametrization of a curve C then the line integral…

Q: Find the equation for the rectifying plane at the point that corresponds to that value of t. r(t) =…

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Q: B) Use Green's Theorem to evaluate /F-dr, where C is the circle r² + y? = 4 and F (r, y) = (y – 2…

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Q: 2. Find the distance between the line with parametric equations ï = 1 + 2t, y = −2+ 4t, z = 4 − 4t…

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Q: Which of the following is dy for the curve dx defined by x° – y³ = 2xy? 3x2-2y а. 2x+3y2 3x2-2y b.…

A: Find the derivative of the given curve and match with the correct option.

Q: Consider the following statement. The parametric equations x = X1 + (x2 - X1)t, y = Y1 + (Y2 – Y1)t…

A: According to question,Given parametric equation,x = x1 + x2 - x1t,andy = y1 + y2- y1t,0 ≤ t ≤1,

Q: A circle with center at the origin and radius equal to a meets the axis of x at A and B. P(a) and…

A: The coordinates of A are (-a,0) and that of P are (a cos α,a sin α)  Therefore,the equation of AP…

Q: An object moves along the curve determined by the parametric equations  x(t) = t−sin(2t) and y(t) =…

A: x(t)=t-sin2t                                         y(t)=t-cos2tdxdt=1-2cos2t…

Q: Show that the work of F = (2³-y³)i + (2³-y³)j on c, the unit circle centered at the origin with…

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Q: Evaluate I = f (z, x, y). dr and C is the helix of r(t) = (cost, sin t, 3t) sketch the curve C.

A: Given,               I=∫Cz, x, y·dr, and C is the helix of r(t)=cost, sint, 3t.

Q: Suppose that for a given curve defined parametrically, dy dx dt = sint. Then dx² dy dt = tant and

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Q: et F(x, y) = (y sin x)i - 3x²j. et D be the unit square (i.e. D = {(x, y): 0≤x≤ 1,0 ≤ y ≤ 1}), and…

A: We have to choose the correct answers of two questions.

Q: Suppose C is the curve given by r(t) = (3 cos(t), -3 sin(t), 4t). Find an equation for the…

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Q: Let F (x, y) = 8Q A. Compute 82 yi+zj z² + y² and let C be the circle r(t) = (cost)i + (sin t) j. 0…

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Q: Let C be circle of radius 1 centered at the origin, oriented counterclockwise. Determine (z)2 dz.

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Q: =2) Calculate & ydx + xz² dy - zy³ dz, where c is the circle x² + y² = 4, Z=3 (conterclockwise)…

A: We will use stokes theorem to find integral

Q: a) Use Green's theorem to compute f F dr where c is a circle of radius R oriented CCW and F(x, y) =…

A: Green's theorem:∫C[Pdx+Qdy]=∫∫T∂Q∂x-∂P∂ydxdy where T is the region bounded by a simple closed curve…

Q: Find the length of the curve defined by the parametric equations t, y = 5 In((t/6)? – 1) I = from t…

A: Given, x = 56t , y = 5lnt62-1 = 5lnt2-36-5ln(36)and 7≤t≤10

Q: Let r(t) = (et, et sin t, et cos t).  Find the equation of the plane that is normal to the curve at…

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Q: b) Calculate dz z² - 1 S ₂ Along the positive direction of the curve |z| = 2 Hint: The curve |z| = 2…

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Q: A curve is given parametrically by=et 2e-t, y = e2t. The tangent t the curve at t = ln 2 is...? a)…

A: Given x = et - 2e-ty = e2tat t = ln2

Q: Find a parametric form for the curve given by y – 2x? = 3, 3 < y< 5. Select one: O a. None of these…

A: The given curve is  y - 2x2 = 3,     3 ≤  y ≤ 5

Q: V7x + 2y – x = y.

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Q: Show that the graph of the parametric equations x = a + (c − a)t, y = b+(d−b)t, t ∈ [0, 1] is a line…

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Q: (*v² + ) ( - 3xy x°y + 5xy ) dy corresponde a: Una expresión que permite calcular dx + -IL (-*y+5y –…

A: We will use the green's theorem to solve the question.

Q: vestigate and ske ² + 2x +8y - 31

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Q: Find the length of the parametric curve: x = 2t + 1; y = t? – 3,0 <t < 5

A: Given that: x=2t+1,  y=t2-3,0≤t≤5To  calculate   dxdt  and   dydt,dxdt=ddt2t+1=2dydt=ddtt2-3=2t

Q: Q2:al Use separation of variables to find the solution of the following Initial Value Problems.…

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