(1 point) Given R(t) = $e^t \cos(4t)i + e^t \sin(4t)j + 4e^tk$ Find the derivative R'(t) and norm of the derivative. R'(t) = ||R'(t)|| = Then find the unit tangent vector T(t) and the principal unit normal vector N(t) T(t) = N(t) =
Added by Juan L.
Close
Step 1
Thus R'(t)=e^t[cos(4t)-4 sin(4t)] i + e^t[sin(4t)+4 cos(4t)] j + 4 e^t k. Show more…
Show all steps
Your feedback will help us improve your experience
Hemraj Kumawat and 97 other Calculus 1 / AB educators are ready to help you.
Ask a new question
Labs
Want to see this concept in action?
Explore this concept interactively to see how it behaves as you change inputs.
Key Concepts
Recommended Videos
Find the position vector R(t) and velocity V(t) given the acceleration A(t) = 80e^{4t} i + 50 cos(5t) j + 6tk and the initial velocity vector V(0) = -i - 3j + 3k and initial position vector R(0) = -i - 2j - k. V(t) = R(t) = Given R(t) = 10ti + 5t^2 j + k Find the derivative R'(t) and norm of the derivative. R'(t) = 10i+10tj ||R'(t)|| = sqrt(100+100t^2) Then find the unit tangent vector T(t) and the principal unit normal vector N(t) T(t) = (10i+10tj)/(sqrt(100+100t^2)) N(t) =
Aman G.
Find the unit tangent and principal unit normal vectors at the given points. $$ \mathbf{r}(t)=\left\langle t, t^{2}\right\rangle \text { at } t=0, t=1 $$
Vector-Valued Functions
Tangent and Normal Vectors
Find the unit tangent vector $\mathbf{T}$ and the principal unit normal vector $\mathbf{N}$ for the following parameterized curves. In each case, verify that $|\mathbf{T}|=|\mathbf{N}|=1$ and $\mathbf{T} \cdot \mathbf{N}=0$ $$r(t)=\langle t, \ln \cos t\rangle$$
Vectors and Vector-Valued Functions
Curvature and Normal Vectors
Recommended Textbooks
Calculus: Early Transcendentals
Thomas Calculus
Watch the video solution with this free unlock.
EMAIL
PASSWORD