Answer to Question #116868 in Calculus for Olivia

Question

For r(t)=⟨tsin(t),e^t,t+π⟩, then r′(t) is equal to
Select one:
a. ⟨sin(t)−tcos(t),e^t,1⟩+c where c is an arbitrary constant vector

b. ⟨sin(t)+tcos(t),e^t,t⟩


c. ⟨cos(t),e^t,π⟩


d. ⟨sin(t)−tcos(t),e^t⟩


e. ⟨sin(t)+tcos(t),e^t,1⟩

Answer 1

r(t) = [tsint, e^t,t+π]

Here d(tsint)/dt = t d(sint)/dt + sint d(t)/dt

= t cost + sint

d(e^t)/dt = e^t;

d(t+π)/dt = 1 since π is constant.

So

r'(t) = [tcost + sint, e^t, 1].

Option e is correct.