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- Find the derivative of the vector function r(t) = (200) r(t) = In (15-t²) i+√4+tj-6e² kFind the derivative of the vector functionr(t)=ta×(b+tc), wherea=⟨3,−2,−3⟩, b=⟨1,3,−2⟩, and c=⟨−2,−4,−4⟩.r′(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.
- For time t > 0, a particle moves with velocity vector given by v (t) = (f (t) , g (t)), where f and g are continuous functions of t. At time t = 3, the particle is at position (-4, 5). Which of the following expressions gives the particle's position at time t = 1? A (-2f (3), –2g (3)) (-4 – 2f (3), 5 – 2g (3)) f (t) dt, -4 - f (t) dt, 5Find the derivative of the vector function r(t) = ta x (b + tc), where a = (-5, 3,2), b = (1,2, –2), and c = r (t) = ( (5, –5, 3).Find the domain of the vector function r(t)= <e-t , (t-5)1/2 , (7-t)1/2.
- Represent the plane curve by a vector-valued function. x2 /16−y2/ 4= 1The equation r(t)=(t+2) i+t2−7 j+(2t) k is the position of a particle in space at time t. Find the particle's velocity and acceleration vectors. Then write the particle's velocity at t=1 as a product of its speed and direction.For time t > 0, a particle moves with velocity vector given by v (t) = (f (t) , g(t)), where f and g are continuous functions of t. At time t 3, the particle is at position (-4, 5). Which of the following expressions gives the particle's position at time t = 1? A (-2f (3), –2g (3)) (-4 – 2ƒ (3) , 5 – 2g (3)) B f (t) dt, -4 – f (t) dt, 5
- Find the domain of the vector-valued function r(t)=ln(t-1)i+Square root 4-tjEvaluate 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) =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 ...