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(1 point) (a) Find as a function of t for the given parametric equations. dx x...
(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 =
(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.
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
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,...
(1 point) Find the length of the curve defined by the parametric equations 3 -1, X = y = 3 ln((t/4)2 – 1) from t = 6 to t = 7.
7. [-12 Points] DETAILS ROGACALCET3 11.1.033. Find parametric equations for the segment joining the given points. (3, 1) and (5, 4) c(t) |),osts 8. [-12 Points] DETAILS ROGACALCET3 11.1.049. Use the formula for the slope of the tangent line to find out for the curve c(t) - (543, 48 - 5) at t = 3. dy dx - 3 9. [-12 Points] DETAILS ROGACALCET3 11.1.062. Find an equation of the tangent line to the curve c(t) - (962 - 6,612...
Find parametric equations for the line that is tangent to the given curve at the given parameter value. r(t) = (5+?) 1+ (2t - 1)]+(31') k, t=to = 3 What is the standard parameterization for the tangent line? X = y = ZE (Type expressions using t as the variable.)
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)
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...