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Q. 02

Expert-verified

Calculus

Found in: Page 720

Book edition 1st

Author(s) Peter Kohn, Laura Taalman

Pages 1155 pages

ISBN 9781429241861

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Short Answer

Examples: Construct examples of the thing(s) described in the following. Try to find examples that are different than any in the reading.
(a) Parametric equations $$x = f(t), y = g(t)$$ on the interval $$[0, 1)$$ that trace the unit circle exactly once clockwise, starting at the point $$(1, 0)$$.
(b) Parametric equations $$x = f(t), y = g(t)$$ on the interval $$[0, 2π)$$ that trace the circle centered at $$(2, −3)$$ with radius 5 exactly once counterclockwise, starting at the point $$(7, −3)$$.
(c) Parametric equations $$x = f(t), y = g(t)$$ whose graph is not the graph of a function $$y = f(x)$$.

(a) $$(cost, -sint)$$

(b) $$(2+5cost, 5sint-3)$$

(c) $$(rcost, rsint)$$

See the step by step solution

Step by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

Step 1. Given Information

Parametric equations $$x = f(t), y = g(t)$$ on the interval $$[0, 1)$$ that trace the unit circle exactly once clockwise, starting at the point $$(1, 0)$$.

Step 2. Explanation

The constructed example can be given as, $$(cost, -sint)$$

Step 3. Given Information

Parametric equations $$x = f(t), y = g(t)$$ on the interval $$[0, 2π)$$ that trace the circle centered at $$(2, −3)$$ with radius 5 exactly once counterclockwise, starting at the point $$(7, −3)$$.

Step 4. Explanation

The constructed example can be given as, $$(2+5cost, 5sint-3)$$

Step 5. Given Information

Parametric equations $$x = f(t), y = g(t)$$ whose graph is not the graph of a function $$y = f(x)$$.

Step 6. Explanation

The constructed example can be given as, $$(rcost, rsint)$$

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