Let C be the part of the curve x? + y² = 1 with y 2 0, oriented counter- clockwise. Evaluate F. dr, where F = ( cos r + x2, y sin r + In(1+ y?)).

Q: For the smooth curve r(t), find the parametric equations for the line that is tangent to r at the…

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Q: Let F = (y – x, ry) and let C be the line segment from (2, –3) to (1, –1). %3D Evaluate F. dr.

A: We wil first equation of parametric equation of line segment

Q: - Use the graphs of = irection in which the curve is traced as t increases. = f(t) and y = g(t) to…

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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: 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: Let C be the circle given by x² + y² = 1. Evaluate √(-2x²y + cos x)dx + (2 xy² + y²e³)dy going in…

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

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Q: 2. Consider the parametric curve r = t + 1, y = t - t. dy (a) Find d.r dy (b) Find da?

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Q: Let f(x, y) = VI+27xy and let C be the curve given by y = 3x' for 0 < x < 2. Compute ſe f ds. (Use…

A: Given- Let fx, y = 1 + 27xy and let C be the curve given by y = 3x3 for 0 ≤ x ≤ 2.  To find- Compute…

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: is the following function analytic (Express your answer in polar form) f(z): = y - ix x² + y²

A: We can solve this using polar form of analytic function

Q: Let f (x, y) = e3x-49). Find the equation for the tangent plane to the graph of f at the point…

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Q: Let x = 3t², y = −2t³ + 18t². dy Determine as a function of t, then find the slope of the parametric…

A: Let To determine  as a function of t, then to find the slope of the parametriccurve at .To…

Q: Find F-dX where C is the curve X(r) = r°I+( 2r+ 1J, 0<I55, and Fxy) = rI+yJ.

A: 9

Q: Compute f ds for the curve specified. f(x, y) = V1 + 9xy, y = x3 for 0 < x < 2.

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Q: П π Find T, N, and k for the plane curve r(t) = 7t i +7 In (cost) j. - <t<2.

A: Since you have uploaded multiple questions according to our guidelines we have solved first question…

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: Q1: Use Green's theorem to evalute f. (xy + y2)dx + x²dy by the curve y = x and y = x2.

A: Given problem:- Use Green's theorem to evaluate ∫c (xy + y2 )dx + x²dy  by the curve y = x and y =…

Q: 10. Find the value of 2 for the parametric curve xx= y = 2t2 -6 at the point (1.-6).

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Q: Prove that for the curve x = 31, y = 3 f², z = 2 8³, 3 (1+21²) 2 p=-o=

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Q: Sketch the following curve

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Q: Suppose (X1, · · · , Xn) with each Xi following exp(θ, 1). Show that X(1) is complete and…

A: In the given problem, we are dealing with a random sample (X1, X2,..., Xn) where each Xi follows an…

Q: Evaluate + 5x)dx + (ye* – 3y²)dy where C is the boundary of the curve given below. -2

A: Detailed explanation mentioned below

Q: 11) Draw the curve F(t) = ß cos(1) 7+ y sin(t)] + tk. Label some key reference points, and indicate…

A: The given parametric curve, r¯t=7 costi⇀+3sintj⇀+tk⇀. To Sketch: The curve and label its points and…