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# In Exercises 27–34 you will use a CAS to | Ch 12.4 - 31CE

ISBN: 9780321717399 65

## Solution for problem 31CE Chapter 12.4

University Calculus: Early Transcendentals | 2nd Edition

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Problem 31CE

In Exercises 27–34 you will use a CAS to explore the osculating circle at a point P on a plane curve where Use a CAS to perform the following steps:a. Plot the plane curve given in parametric or function form over the specified interval to see what it looks like.b. Calculate the curvature of the curve at the given value using the appropriate formula from Exercise 5 or 6. Use the parametrization x = t and y = f(t) if the curve is given as a functionc. Find the unit normal vector N at t0. Notice that the signs of the components of N depend on whether the unit tangent vector T is turning clockwise or counterclockwise at t = t0. (See Exercise 7.)d. If C = ai + bj is the vector from the origin to the center (a, b) of the osculating circle, find the center C from the vector equation The point P(x0, y0) on the curve is given by the position vector r(t0).e. Plot implicitly the equation of the osculating circle. Then plot the curve and osculating circle together. You may need to experiment with the size of the viewing window, but be sure it is square.

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##### ISBN: 9780321717399

The full step-by-step solution to problem: 31CE from chapter: 12.4 was answered by , our top Calculus solution expert on 08/23/17, 12:53PM. This full solution covers the following key subjects: curve, Vector, osculating, circle, given. This expansive textbook survival guide covers 113 chapters, and 6504 solutions. University Calculus: Early Transcendentals was written by and is associated to the ISBN: 9780321717399. The answer to “In Exercises 27–34 you will use a CAS to explore the osculating circle at a point P on a plane curve where Use a CAS to perform the following steps:a. Plot the plane curve given in parametric or function form over the specified interval to see what it looks like.b. Calculate the curvature of the curve at the given value using the appropriate formula from Exercise 5 or 6. Use the parametrization x = t and y = f(t) if the curve is given as a functionc. Find the unit normal vector N at t0. Notice that the signs of the components of N depend on whether the unit tangent vector T is turning clockwise or counterclockwise at t = t0. (See Exercise 7.)d. If C = ai + bj is the vector from the origin to the center (a, b) of the osculating circle, find the center C from the vector equation The point P(x0, y0) on the curve is given by the position vector r(t0).e. Plot implicitly the equation of the osculating circle. Then plot the curve and osculating circle together. You may need to experiment with the size of the viewing window, but be sure it is square.” is broken down into a number of easy to follow steps, and 201 words. This textbook survival guide was created for the textbook: University Calculus: Early Transcendentals , edition: 2. Since the solution to 31CE from 12.4 chapter was answered, more than 226 students have viewed the full step-by-step answer.

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