4. (12) Consider the parametric equations. Find the points with a horizontal or vertical tangent line by providing their coordinates. (x = 3sin(2t) ly = 2 cos(t) ost s 21,
1. a. Consider the curve defined by the following parametric equations: r(t) = et-e-t, y(t) = et + e-t where t can be any number. Determine where the particle describing the curve is when tIn(3) In(2). 0, ln(2) and In(3). Split up the work among your group Onex, vou l'ave found i lose live polnia, try to n"惱; wbai ille wlu le curve "u"ht lex k like. b. Verify that every point on the curve from the previous problem solves...
Consider the parametric equations below. x = 2 + 4t y = 1-t2 (a) Sketch the curve by using the parametric equations to plot points. Indicate with an arrow the direction in which the curve is traced as t increases.(b) Eliminate the parameter to find a Cartesian equation of the curve. y = _______ Consider the parametric equations below. x = 3t - 5 y = 2t + 4 (a) Sketch the curve by using the parametric equations to plot points. Indicate with an arrow the...
Let the curve C in the (x, y)-plane be given by the parametric equations x = e + 2, y = e2-1, tER. (a) Show that the point (3,0) belongs to the curve C. To which value of the parameter t does the point (3,0) correspond? (b) Find an expression for dy (dy/dt) without eliminating the parameter t, i.e., using de = (da/dt) (c) Using your result from part (b), find the value of at the point (3,0). (d) From...
please answer both
(12(8 pts) Find parametric equations of the line through the point (2, -1,3) and perpendicular to the line with parametric equations 1-t,y 4- 2t and 3+ t and perpendicular to the line with parametric equations 3+t,y 2-t and z 3+2t. (13)(8 pts) Find the unit tangent vector (T(t) for the vector function r(t) - costi+3t j+ 2sin 2t k at the point where t 0
(12(8 pts) Find parametric equations of the line through the point (2,...
(a) Given the parametric equations x = 5t2 −10t, y = t5 find dy/dx. (b) Find the (x,y) coordinate point(s) where the curve has a vertical tangent.
Given the parametric curve x = 3t – tº, y = 3ta. (a) Find all x and y intercepts. (b) Find all points (x, y) where there is a vertical or horizontal tangent. (c) Put this information together in a chart to determine the intervals of increase and decrease and use this to sketch the curve.
4. Tired from the long week, with the amusement park and the wok and dinner plate designs, you retreat to be in peace and study parametric equations. A curious leaflike curve called the "folium of Descartes" catches your eye; it is defined by the parametric equations 3t 3t2 (a) (4 points) Show that if the point (a, b) lies on the curve, then so does (b, a); that is, the curve is symmetric with respect to the line y a....
Consider the following parametric equations. a. Eliminate the parameter to obtain an equation in x and y b. Describe the curve and indicate the positive orientation. x=5 cost, y = 13 + 5sint; 0 ≤ t ≤ 2π a. Eliminate the parameter to obtain an equation in x and y.
1. (3) Find parametric equations for the tangent line to the curve x(t) y(t) = 7+3 when t = 1. 5 3+212