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Chapter 11: Q. 2 (page 901)

Sketching vector functions: Sketch the following vector functions.
$r (t) = (\cos t, t) \in ℝ$

Short Answer

Expert verified

$r (t) = (\cos t, t) \in ℝ$

Step by step solution

Step 1. Given information

$r (t) = (\cos t, t) \in ℝ$

Step 2. Sketching the vector

x=cos x, y=x

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Most popular questions from this chapter

Let y = f(x). State the definition for the continuity of the function f at a point c in the domain of f .

For each of the vector-valued functions, find the unit tangent vector.

r (t) = (\cos (α t), \sin (α t))

Let $r_{1} (t)$ and $r_{2} (t)$ both be differentiable three-component vector functions. Prove that

\frac{d}{d t} (r_{1} (t) \times r_{2} (t)) = r_{1}^{'} (t) \times r_{2} (t) + r_{1} (t) \times r_{2}^{'} (t)

(This is Theorem 11.11 (d).)

Imagine that you are driving on a twisting mountain road. Describe the unit tangent vector, principal unit normal vector, and binomial vector as you ascend, descend, twist right, and twist left.

Let Cbe the graph of a vector-valued function r. The plane determined by the vectors $N (t_{0}), B (t_{0})$ and containing the point $r (t_{0})$ is called the normal plane forC at $r (t_{0})$ . Find the equation of the normal plane to the helix determined by $r (t) = < \cos t, \sin t, t >$ for $t = π$ .

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Sketching vector functions: Sketch the following vector functions.r(t)=(cost,t)∈ℝ

Short Answer

Step by step solution

Step 1. Given information

Step 2. Sketching the vector

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Sketching vector functions: Sketch the following vector functions.
$r (t) = (\cos t, t) \in ℝ$