Given the vector-valued functions u(t) =ee (t) 5ti+4t2 – k = d + – tk find (u(t) (t)) when t = 1. dt Find the unit tangent vector to the curve defined by (t) = (1t, -4t, √42) at t = 0. T(0) Use the unit tangent vector to write the parametric equations of a tangent line to the curve at t = 0. x(t) = y(t) = z(t) =

Let u(t)=9t³i + (t²-1)j- 4k. Compute the derivative of the following function. u (tª - 2t) Select the correct choice below and fill in the answer box(es) to complete your choice. A. The derivative is the scalar function B. The derivative is the vector-valued function i + + ( )j + (k.

Find the derivative of the vector function r(t) = (200) r(t) = In (15-t²) i+√4+tj-6e² k

Evaluate the vector-valued function at each given value of t. (If you need to use At, enter Deltat.) r(t) = i - (t - 4)j (a) r(4) = 8 (b) r(0) (c) r(s+ 4) = (ar - 4at)i- 2aj (d) r(2 + At) - r(2) =

Find the domain of the vector function r(t)=⟨ln⁡(19t),sqrt(t+8),1/sqrt(7−t)⟩ using interval notation.

Let u(t) = 2t°i+ (ť - 1)j-8k. Compute the derivative of the following function. (1" +71) u(1) Select the correct choice below and fill in the answer box(es) to complete your choice. O A. The derivative is the scalar function O B. The derivative is the vector-valued function ()i+ (Dj+ ( k. Click to select and enter your answer(s) and then click Check Answer. Clear All All parts showing

Let u(t) = 7t³i+ (t² - 9) j - 7k and v(t) = ei + 3e j -e³t k. Compute the derivative of the following function. u(t) • v(t) Select the correct choice below and fill in the answer box(es) to complete your choice. OA. The derivative is the vector-valued function (i+j+k. B. The derivative is the scalar function ...

Find the second derivative of the vector-valued function 7(t) = (6t + 4 sin(t))i + (5t + 7 cos(t))j 7(t) = %3D

State whether the following derivatives of vector-valued functionsr1(t) and r2(t) are scalars or vectors:d/dt r1(t) × r2(t)

3, Let u(t) = 2t°i+ (t- 1)j- 8k. Compute the derivative of the following function. (118 + 7t) u(t) Select the correct choice below and fill in the answer box(es) to complete your choice. The derivative is the vector-valued function ( Di+ ( Di+ ( k. O B. The derivative is the scalar function