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Chapter 11: Q. 30 (page 880)

Find the unit tangent vector and the principal unit normal vector at the specified value of t.
$r (t) = (a \sin h t, b \cos h t) W h e r e a a n d b a r e p o s i t i v e, t = 0$

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n xm m x

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Most popular questions from this chapter

Evaluate and simplify the indicated quantities in Exercises 35–41.
$(\sin t, \cos t) . (\cos t, - \sin t)$

$Let t = f (τ) be a differentiable real - valued function of τ, and let r (t) be a differentiable vector function with either two or three components such that f (τ) is in the domain of r for every value of τ on some interval I . Find \frac{d (r (f (τ)))}{d τ} .$

Let $f (t)$ be a differentiable scalar function and $r (t)$ be a differentiable vector function. Prove that $\frac{d}{d t} (f (t) r (t)) = f' (t) r (t) + f (t) r' (t)$ . (This is Theorem 11.11 (b).)

Explain why the graph of every vector-valued function $r (t) = (\cos t, \sin t, \cos t)$ lies on the intersection of the two cylinders $x^{2} + y^{2} = 1 and y^{2} + z^{2} = 1 .$

Let $t = f (τ)$ be a differentiable real-valued function of $τ$ , and let $r (t)$ be a differentiable vector function with three components such that $f (τ)$ is in the domain of $r$ for every value of $τ$ on some interval I. Prove that $\frac{d r}{d τ} = \frac{d r}{d t} \frac{d t}{d τ}$ . (This is Theorem 11.8.)

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Find the unit tangent vector and the principal unit normal vector at the specified value of t.r(t)=(asinht,bcosht)Whereaandbarepositive,t=0

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Find the unit tangent vector and the principal unit normal vector at the specified value of t.
$r (t) = (a \sin h t, b \cos h t) W h e r e a a n d b a r e p o s i t i v e, t = 0$