ind parametric equations for the tangent line to the curve with the given parametric equations at the specified point. X = V t² + 35, y = In(t² + 35), z = t, (6, In(36), 1) x(t), y(t), z(t)) =
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- Find parametric equations for the tangent line to the curve with the given parametric equations at the specified point ->(5,0,0). x=5e^t, y=te^4t,z=te^(t^5)Find parametric equations for the tangent line to the curve with the given parametric equations at the specified point. x = t2 + 24 , y = ln(t2 + 24), z = t; (5, ln(25), 1)Find parametric equations for the tangent line to the curve with the given parametric equations at the specified point. x = 3 ln(t), y = 4t1/2, z = t3; (0, 4, 1)
- Find a parametric equation for the path of a particle that moves halfway around the circle (x^2)+(y-1)^2 = 9 counterclockwise, if the particle starts at (0,4). Let x and y be in terms of t for t between 0 and pi.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 = 1 + 12sqrt(t), y = t5 − t, z = t5 + t; (13, 0, 2)
- A curve has the following parametric equations with parameter t. x=2t-1/2t and y=2t+1/2t. Find dy/dx and d²y/dx² in terms of t. And obtain the coordinates of stationary points of the curve and determine the nature of the points.Consider the parametric equations for a curve in the xy-plane given by: x = t^3 - 3t y = t^2 - 2 Find the equation of the tangent line to the curve at the point where t = 2.Find a parametric description for the curve y=4-x^2 from (-2, 0) to (2, 0) such that t=0 corresponds to (-2, 0)