For the curve defined by the parametric equations [x = 3 + sect y=3+5tant Find the first derivative: dx 5 sec²(t) sec (t) tan(t) Find the second derivative: d²y dx² 5 cot" (t) X 3π Determine whether the curve is concave up or concave down at t = 7 -: Concave up
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Calculus with Parametric Curves
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- Write parametric equations for a cycloid traced by a point P on a circle of radius a as the circle rolls along the x -axis given that P is at a maximum when x=0.Find the second derivative of y with respect to x from the parametric equations given. Pls show the detailed solution. Thank youof the parametric equations = and y = 5Vis. The derivative
- What curve do the parametric equations x= e', y= e " represent? Find the slope of the tangent line to this curve at the point (3, 9). Find the concavity of the curve at this point.Find the slope of the parametric curve x = -6t²-1, y = 2t³, for -∞to the curve given by the parametric equationIt is drawn at the point t = ? / 4 tangent and normalFind the equation. (Find it with the help of derivative.)How to generate the curve over the interval for the parameter t then how to find the equivalent rectangular equationConsider the parametric equation x= 10-t2 , y= t3- 12t, -5 ≤ t ≤ 5. These equations define a curve. Find the points on the curve where the tangent line is vertical. Find the equation of the tangent line to the curve at the point(1, 9)Find all points (if any) of horizontal and vertical tangency to the curve x = 6+2 cose, y = -2+ sine. Select one: a. horizontal tangent: (8,-2), vertical tangent: (6, -1) b. horizontal tangents: (8, -2), (4, -2), vertical tangents: (6, -1), (6,-3) C. horizontal tangents: (6,-3), (6,-3), vertical tangents: (8,-2), (4, -2) d. horizontal tangent: (6, -1), vertical tangent: (8,-2) e. horizontal tangents: (6, -1), (6, -3), vertical tangents: (8,-2), (4,-2)A curve is given by the parametric equations x = t¹2t², y = 3t¹ - 7t³, -2Sketch the plane curve represented by the given parametric equation x = 2 sin t - 3, y = 2 sin t + 1. Then use interval notation to give the relation’s domain and range.Find and simplify dy/dx and d'y/dx2, and find the slope and concavity (if possible) at the given value of the parameter. (If an answer does not exist, enter DNE.) All work must be shown evaluating and simplifying each derivative. Parametric Equations Point Vt, y = Vt - 1 X = v t = 5 dy dx d?y dx2 = slope: concavity: ---Select---SEE MORE QUESTIONSRecommended textbooks for youTrigonometry (MindTap Course List)TrigonometryISBN:9781337278461Author:Ron LarsonPublisher:Cengage LearningAlgebra and Trigonometry (MindTap Course List)AlgebraISBN:9781305071742Author:James Stewart, Lothar Redlin, Saleem WatsonPublisher:Cengage LearningTrigonometry (MindTap Course List)TrigonometryISBN:9781337278461Author:Ron LarsonPublisher:Cengage LearningAlgebra and Trigonometry (MindTap Course List)AlgebraISBN:9781305071742Author:James Stewart, Lothar Redlin, Saleem WatsonPublisher:Cengage Learning