Find the length of the curve x=2/3t^3 , y=4t^2 on 0<=t<=3
For the following equations : x= 2t^2 , y = 3t^2 , z= 4t^2 ; 1 <=t <=3 A) write the position vector and tangent vector for the curve with the parametric equations above B) Find the length function s (t) for the curve C) write the position vector as a function of s and verify by differentiation that this position vector in terms of s is a unit tangent to the curve.
(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 =
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.
(a) Find the unit tangent vector, T(t) and the unit normal vector, N(t), for the space curve r(t) cos(4t), sin(4t), 3t >. (b) From part (a), show that T(t) and N(t) are orthogonal (a) Find the unit tangent vector, T(t) and the unit normal vector, N(t), for the space curve r(t) cos(4t), sin(4t), 3t >. (b) From part (a), show that T(t) and N(t) are orthogonal
(3) Find the area bounded by the curve x(t) = 3t-t2, y(t) = 3.li and the y-axis. 3 N 1 2
Question 3: Find the length of the curve ř(t) = (4t, -t?, 2t3) between t = 0 and t = 1 and the curvature of the curve at the origin.
3. Find the length of the curve y = y=for 0 < x < 2.
Find y(t) solution of the initial value problem 3t y? Y' – 6 y3 – 4t² = 0, y(1) = 1, g(1)=1, t > 0.
Find the exact length of the curve. x = t 2 + t' y = In(2 + t), 0<t< 5 1.2986 Need Help? Read It Watch It Talk to a Tutor
Marks 4 3. Find the length of the curve x t + cos t, y= t - sin t on the interval 0<t<2m. Marks 4 3. Find the length of the curve x t + cos t, y= t - sin t on the interval 0