Question

2- Find the vectors \textbf{t}(s), \textbf{b}(s), \textbf{n}(s) and the functions K(s), \tau(s) of the curves: i)The circle \textbf{a}(s) = (a \cos{\frac{s}{a}}, a \sin{\frac{s}{a}}, 0), $a > 0$. ii) \textbf{a}(t) = (t, t^2, t^3)

          2- Find the vectors \textbf{t}(s), \textbf{b}(s), \textbf{n}(s) and the functions K(s), \tau(s) of the curves:
i)The circle \textbf{a}(s) = (a \cos{\frac{s}{a}}, a \sin{\frac{s}{a}}, 0),  $a > 0$.
ii) \textbf{a}(t) = (t, t^2, t^3)

2- Find the vectors t(s), b(s), n(s) and the functions K(s), τ(s) of the curves:
i)The circle a(s) = (a cos(s)/(a), a sin(s)/(a), 0), a > 0.
ii) a(t) = (t, t^2, t^3)

Added by David R.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Adi S

06/20/2023

Step 1

The unit tangent vector is given by: \[t(s) = \frac{\alpha'(s)}{||\alpha'(s)||}\] where $\alpha'(s)$ is the derivative of $\alpha(t)$ with respect to $t$. Show more…

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2- Find the vectors t(s),b(s),n(s) and the functions K(s), au (s) of the curves: ii) alpha (t)=(t,t^(2),t^(3)) 2 Find the vectors t(s) , b(s), n(s)and the functions K (s), t(s) of the curves: i)The circle a(s) = (acos , a sin ,0), a a>0. ii) a(t)=(t,t2,t3)