(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.
(a) Given the parametric equations x = 5t2 −10t, y = t5 find dy/dx. (b) Find...
(1 point) (a) Find as a function of t for the given parametric equations. dx x t-ps у 4 - 31 dy dx = (b) Find dy as a function of t for the given parametric equations. dx X 5 - 4 -1 у dy dx =
1a) Find dy/dx x = te', y = t + sin t b) Find dy/dx and d’y/dx2 for which t is curve concave upward x = x3 + 1, y = t - c)Find the points on the curve where the tangent is horizontal or vertical. Draw the graph x = 13 – 3t, y = t3 – 312 d) Find the area enclosed by the x-axis and the curve x = t3 + 1, y = 2t – t?....
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...
find parametric equations for the tangent line to the curve with the given parametric equations at the specified point. x=10cost, y=10sint, z=8cos2t; (5sqrt3,5,4)
Find parametric equations for the tangent line to the curve with the given parametric equations at the specified point. x = 4 In(t), y = 6/t, z = t4; (0,6, 1) x(t), y(t), z(t) = X
Find dy/dx. Find the points on the curve where the tangent is horizontal or vertical. x = t3 - 3t, y = t2 - 6
(1 point) (a) Find dy du as a function of t for the given parametric equations. 2 = t- +5 y 6 – 2t dy dc (b) Find dy as a function of t for the given parametric equations. dc 2 4t – 6 +5 – +9 Y dy da =
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.
2. Consider the parametric equations x = 5 - 12, y = 13 - 481 a. Find , and determine for what values oft is the curve concave up. and when is it concave down. 2 .- der2 b. Find where is the tangent line horizontal, and where is it vertical.
(5,3,-2) Evaluate the integral y dx + x dy + 4 dz by finding parametric equations for the line segment from (2,1,5) to (5,3,-2) and evaluating the line integral of (2,1,5) F = yi + x3 + 4k along the segment. Since F is conservative, the integral is independent of the path. (5,3,-2) y dx + x dy + 4 dz= (2,1,5)