Consider the parametric curve given by x(t) = t^2 − 2, y(t) = 2t^3 + 3, What is the length of the arc from the point (−1, 1) to the point (2, −13)
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Consider the parametric curve given by x(t) = t^2 − 2, y(t) = 2t^3 + 3,...
Consider the parametric curve given by x(t) = 16 sin3(t), y(t) = 13 cos(t) − 5 cos(2t) − 2 cos(3t) − cos(4t), where t denotes an angle between 0 and 2π. (a) Sketch a graph of this parametric curve. (b) Write an integral representing the arc length of this curve. (c) Using Riemann sums and n = 8, estimate the arc length of this curve. (d) Write an expression for the exact area of the region enclosed by this curve.
2t from Find the length of the parametric curve given by r(t) = 2 – logt and y(t) t=l to t= e.
Consider the following parametric equations. x=2t-3, y = 8t3 ;- 2 ≤ t ≤ 2
(6pts) Consider the curve given by the parametric equations x = cosh(4t) and y = 4t + 2 Find the length of the curve for 0 <t<1 M Length =
Question 11 Find the length of the curve with parametric equations x = 2t, y = 3t, where 0 <t < 1. 10 42-2 O 4V2 - 1 22-1 4/ Question 12 True or false: y=x cos x is a solution of the differential equation y + y = -2 sin x True False
25. Given the following parametric curve X(t) = -1 + 3 cos(t) y(t) = 1 + 2 sin(t) 0<t<21 a) Express the curve with an equation that relates x and y. 7C b) Find the slope of the tangent line to the curve at the point t c) State the pair(s) (x,y) where the curve has a horizontal/vertical tangent line. 27.A particle is traveling along the path such that its position at any time t is given by r(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...
Consider the parametric curve F(t) = (2+1 - 2)i+2 4 13 (a) (10 points) Evaluate SF(t)dt. (b) (10 points) Show that the arc length parameter measured from the point (2,0) is given by s = 4 tan-(t). (c) (10 points) By substituting t = tan (4) verify that F(t) parameterizes a circle of radius 2. What is the curvature?
Question 8 (10 points) Consider the following parametric curve: æ(t) = ť- 2t+2, y(t) = ť- 2+ + 2t - 3 In the FIRST answer box, write the SLOPE of the tangent line at t-2 and in the SECOND answer box, write the EQUATION of the tangent line at t-2. You do NOT need to show work. -
Question 8 (10 points) Consider the following parametric curve: æ(t) = ť- 2t+2, y(t) = ť- 2+ + 2t - 3 In the FIRST answer box, write the SLOPE of the tangent line at t-2 and in the SECOND answer box, write the EQUATION of the tangent line at t-2. You do NOT need to show work. -