Solution: Finding Vectors In Exercises 3742, find and at the given time for the space

Chapter 12, Problem 41

(choose chapter or problem)

Finding Vectors In Exercises 37-42, find T(t), N(t), \(a_{\mathrm{T}}\), and \(a_{\mathrm{N}}\) at the given time t for the space curve r(t). [Hint: Find a(t), T(t), \(a_{\mathrm{T}}\), and \(a_{\mathrm{N}}\). Solve for N in the equation \(a(t)=a_{\mathrm{T}} \mathbf{T}+a_{\mathrm{N}} \mathbf{N}\)

Vector-Valued Function                                                    Time

\(\mathbf{r}(t)=e^{t} \sin t \mathbf{i}+e^{t} \cos t \mathbf{j}+e^{t} \mathbf{k}\)          t = 0

Text Transcription:

a_T

a_N

a(t)=a_T T + a_N N

r(t)=e^t sin ti+ e^t cos tj + e^tk

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