Q: Given x=3( θ-sin θ) and y=3( 1-cos θ) a. Trace the parametric curve b. Find dy/dx
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Q: 1.Given x=3( θ-sin θ) and y=3( 1-cos θ) a. Trace the parametric curve b. Find dy/dx c. Find…
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A: Please refer the attached image for complete solution.
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- 1.Given x=3( θ-sin θ) and y=3( 1-cos θ) a. Trace the parametric curve b. Find dy/dx c. Find d/dx2 2. If z=ln (x-y) +tan (x+y) find zxx and zyy(a) Find the exact area of the surface obtained by rotating the curve y = e^x about thex-axis over the interval 0 ≤ x ≤ 1.(b) Determine the length of the parametric curve given by the following set ofparametric equations.x = 3 cos t − cos 3t, y = 3 sin t − sin 3t, 0 ≤ t ≤ πYou may assume that the curve traces out exactly once for the given range of t.(a) By eliminating the parameter, sketch the trajectory over the time interval 0 ≤ t ≤1 of the particle whose parametric equations of motion are x = cos (πt), y =sin(πt)(b) Indicate the direction of motion on your sketch.(c) Make a table of x-and y-coordinates of the particle at times t = 0, 0.25, 0.5, 0.75, 1.(d) Mark the position of the particle on the curve at the times in part (c), and label those positions with the values of t.
- 7. a. Find the parametric equations for the surface generated byrevolving the curve y = sin x about the x-axis. b. Using the parametric equations from part a. set up but do NOTevaluate an integral that will give the surface area of that portion ofthe surface for which 0 ≤ x ≤ π. c. . Find the equation of the tangent plane to the parametric surfacein part a. at the point (x, y, z) = (pi/6, 1/2, 0)Fast pls solve this question correctly in 5 min pls I will give u like for sure Anu Integrate f (x, y) = y over the top half of the circle (x − 1)2 + y2 = 1 in two ways a) In rectangular coordinates. b) In polar coordinatesFind parametric equations for the tangent line to the curve with the given parametric equations at the specified point. x = e−8t cos(8t), y = e−8t sin(8t), z = e−8t; (1, 0, 1)
- (a) Determine x(t) and y(t) a pair of parametric equations for the graph of y = cosh x. (b) Calculate dy/dx using the parametric equations from above. (c) Set up but do not solve the integral to calculate the arc length (s) of the curve betweenx = −1 and x = 1. (d) Estimate the arc length s from the question above using a Riemman Sum with n = 20and midpoints. Please show work.1.Given x=3( θ-sin θ) and y=3( 1-cos θ) a. Trace the parametric curve b. Find dy/dx c. Find d/dx210.2 37)Find the area enclosed by the given parametric curve and the y-axis.
- 1. Find parametric equations for the tangent line to the curve with the given parametric equations at the specified point. x= e−2t cos(2t), y = e−2t sin(2t), z = e−2t; (1, 0, 1) 2. Find parametric equations for the tangent line to the curve with the given parametric equations at the specified point. x = e−2t cos(2t), y = e−2t sin(2t), z = e−2t; (1, 0, 1) 3. Reparametrize the curve with respect to arc length measured from the point where t = 0 in the direction of increasing t. (Enter your answer in terms of s.) r(t) = 4t i + (5 − 2t) j + (1 + 3t) kIf the parametric form of a curve is: x(t) = cos (2 pi t)y(t) = sin (2 pi t) Compute the cordinates of the point when t=0.25. What is the x-coordinate of the initial point? Round your answer to 3 decimal places, if needed.Find parametric equations for the tangent line to the curve with the given parametric equations at the specified point. x=2e^t,y=te^2t,z=te^t^5;(2,0,0)