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22) I would some help to find parametric equations for the tangent line to the curve
with the given parametric equations at the specified point, please?
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- 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) kFind 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)Find parametric equations for the tangent line to the curve with the given parametric equations at the specified point. x=e^(-3t) cos (8t) y = e^-3t sin (8t) z = e^-3t (1,0,1)
- 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)Find parametric equations for the tangent line to the curve with the given parametric equations at the specified point. x=4et,y=te2t,z=tet^2;(4,0,0) Solve x(t), y(t), z(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)
- Find parametric equations for the tangent line to the curve with the given parametric equations at the specified point. x = 1 + 4sqrt t ,y=t^4-t, z=t^4 +t; (5,0,2)Find parametric equations for the tangent line to the curve with the given parametric equations at the specified point. x = 6 cos(t), y = 6 sin(t), z = 8 cos(2t), 3 3 , 3, 4 (x(t), y(t), z(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.
- a)lim (e^-x)(x^2+sinh(x+2)) x->∞ b) Find the point where the tangent to the curve defined by the parametric equations x=t^4-2t^2, y=3t^4-4t^3, 0<t≤4 has a slope of 2.Exercise1 :1) Sketch the curve defined by the parametric equations:x = 2t2 + t ; y = t − 2; 2) Find the caratesian equation for the curvex = 2t2 + t ; y = t − 2; Exercise2 :What curve is represented by the following parametric equations ?x = sin(t). ; y = cos(2t) ; 0 ≤ t ≤ 2π you can use cos(2t) = 1 − sin2(t) Exercise3 : A curve C is defined by the parametric equtions:a) Find the equation of tangent line at the point (0; 0 of this curve. b) At what points the curve has a horizontal tangent ? c) At what points the curve has a vertical tangent ? d) Determine where the curve is concave upward or downward ? Exercise4 :a) Compute dy/dx when:x = θ + cosθ ; y = θ − sinθ b) Compute d^2y/dx^2 , when:x = θ + cosθ ; y = θ − sinθ c) Find the tangent at the point θ = π/3 of:x = θ + cosθ ; y = θ − sinθ d) At what points the curve has a horizontal tangent ? when is it vertical ? Exercise5 :1) Find the area of the cycloid x = rcosθ ; y =…Find parametric equations for line that is tangent to the curve x=cost, y=sint, z=t at the point(cos(4π/6),sin(4π/6),4π/6) Parametrize the line so that it passes through the given point at t=0.