Find the Derivative of a Vector-Value Function Find 7' (t), given r(t) = ( 2, -4e4t, 5 sin(t)). 7' (t) = Find the Derivative of a Vector-Value Function Find '(t), given r(t): = 7'(t) = Question Help: Video (4et, 5 sin( 3t), 4 cos( 2t)). Find the Derivative of a Vector-Value Function Find '(t), given r(t): = (3 ln(4t), 4et, - 3t). 7'(t) = Question Help: Video Find the Derivative of a Vector-Value Function Find '(t), given r(t) r' (t) = = Question Help: Video 5t 2 - 4 t - 2t 4' - 2t - 1 Find the Derivative of a Vector-Value Function Find 7'(t), given 7'(t) = ( t ln(3t), 5 sin( 4t + 1), 3te5t). '(t) = Question Help: Video Submit Question Find the Derivative of a Vector-Value Function Given the vector-valued functions (t) = ei + etj + 2tk v(t) 5ti + 2tj 3k = find - ((t) v(t)) when t - dt d -( v)( 2) = = dt Question Help: Video - 2. Find the Derivative of a Vector-Value Function Find the second derivative of the vector-valued function F(t) = (3t+ 6 sin(t))i + (7t + 3 cos (t))] 7''(t) = Question Help: Video = Submit Question Tangent Vector, Tangent Line, and Angle between 2 curves Let 7' (t) = (3t 2, t 3t, 3t). Find the line (L) tangent to r(t) at the point (10, L: (x, y, z) = Question Help: Video Submit Question +t 56, 24) Tangent Vector, Tangent Line, and Angle between 2 curves Let (t) (t +4, 3et, 2e-2t). Find the line (L) tangent to r(t) at t = 1. = L: (x, y, z): = Question Help: Video Submit Question +t Tangent Vector, Tangent Line, and Angle between 2 curves The curves (t) = (2t, t, t5) and r2(t) = (sin(4t), sin(2t), t) intersect at the origin. Find the acute angle of intersection (0) in degrees. 0 = Question Help: Video Submit Question Tangent Vector, Tangent Line, and Angle between 2 curves The curves f(x) = x + 3x 1 and g(x) Find the acute angle of intersection in degrees. 0 = Question Help: Video Submit Question = - 4x + 17 intersect at the point (2, 9). Tangent Vector, Tangent Line, and Angle between 2 curves Find the positive t when the vector r(t) t = Submit Question = (2t, 10t, 7t 4) is perpendicular to r(t). Find the Unit Tangent Vector Let r(t) = (2t 5, 4e5t, 2 sin(4t)) Find the unit tangent vector T(t) at the point t = 0. Round to 4 decimal places. T(0) = Question Help: Video Submit Question Find the Unit Tangent Vector Find the unit tangent vector to the curve defined by r(t) = ( 3t, 5t, 9 ) at t = : 2. T(2) = Question Help: Video Submit Question Find the Unit Tangent Vector Find the unit tangent vector to the curve defined by r(t) = (4 cos(t), 4 sin(t), 5 sin (t)) at t = (7) 3 Question Help: Video = Submit Question . Find the Integral of a Vector-Value Function 3t Let r(t) = (t + 1, 5et, 5 sin( 2t)). fr(t)dt (don't include the +C) Find fr(t)dt = {\ VEL. 1) + C Find the Integral of a Vector-Value Function Let F(t) = ( 1 3,5 cos(3t), 3t +3 3). t fr(t)dt fr(t)dt = ( Find )dt (don't include the +C) + C Find the Integral of a Vector-Value Function 4t Let F(t) = ( 1 ^ 4, Vt 5, 2e). Evaluate the definite integral. t 13 [1 F(t)dt = { Submit Question