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Get Full Access to Calculus: Early Transcendental Functions - 6 Edition - Chapter 12.2 - Problem 3
Get Full Access to Calculus: Early Transcendental Functions - 6 Edition - Chapter 12.2 - Problem 3

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# ?Differentiation of Vector-Valued Functions In Exercises 1-6, find r’(t), $$\mathrm{r}\left(t_{0}\right)$$, and $$\mathrm{r’}\left(t_{0}\right)$$ for t ISBN: 9781285774770 141

## Solution for problem 3 Chapter 12.2

Calculus: Early Transcendental Functions | 6th Edition

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Problem 3

Differentiation of Vector-Valued Functions In Exercises 1-6, find r’(t), $$\mathrm{r}\left(t_{0}\right)$$, and $$\mathrm{r’}\left(t_{0}\right)$$ for the given value of $$t_{0}$$. Then sketch the plane curve represented by the vector-valued function, and sketch the vectors $$\mathrm{r}\left(t_{0}\right)$$, and $$\mathrm{r’}\left(t_{0}\right)$$. Position the vectors such that the initial point of $$\mathrm{r}\left(t_{0}\right)$$ is at the origin and the initial point of $$\mathrm{r’}\left(t_{0}\right)$$ is at the terminal point of $$\mathrm{r}\left(t_{0}\right)$$. What is the relationship between $$\mathrm{r’}\left(t_{0}\right)$$ and the curve?

$$\mathbf{r}(t)=\cos t \mathbf{i}+\sin t \mathbf{j}, \quad t_{0}=\frac{\pi}{2}$$

Text Transcription:

r(t_0)

r’(t_0)

r(t)=cos ti+sin tj, t_0 pi/2

Step-by-Step Solution:

Step 1 of 5) For radon-222 gas, t is measured in days and k = 0.18. For radium-226, which used to be painted on watch dials to make them glow at night (a dangerous practice), t is measured in years and k = 4.3 * 10-4

Step 2 of 2

##### ISBN: 9781285774770

Since the solution to 3 from 12.2 chapter was answered, more than 253 students have viewed the full step-by-step answer. The answer to “?Differentiation of Vector-Valued Functions In Exercises 1-6, find r’(t), $$\mathrm{r}\left(t_{0}\right)$$, and $$\mathrm{r’}\left(t_{0}\right)$$ for the given value of $$t_{0}$$. Then sketch the plane curve represented by the vector-valued function, and sketch the vectors $$\mathrm{r}\left(t_{0}\right)$$, and $$\mathrm{r’}\left(t_{0}\right)$$. Position the vectors such that the initial point of $$\mathrm{r}\left(t_{0}\right)$$ is at the origin and the initial point of $$\mathrm{r’}\left(t_{0}\right)$$ is at the terminal point of $$\mathrm{r}\left(t_{0}\right)$$. What is the relationship between $$\mathrm{r’}\left(t_{0}\right)$$ and the curve?$$\mathbf{r}(t)=\cos t \mathbf{i}+\sin t \mathbf{j}, \quad t_{0}=\frac{\pi}{2}$$ Text Transcription:r(t_0)r’(t_0)r(t)=cos ti+sin tj, t_0 pi/2” is broken down into a number of easy to follow steps, and 83 words. This full solution covers the following key subjects: . This expansive textbook survival guide covers 134 chapters, and 10738 solutions. Calculus: Early Transcendental Functions was written by and is associated to the ISBN: 9781285774770. The full step-by-step solution to problem: 3 from chapter: 12.2 was answered by , our top Calculus solution expert on 11/14/17, 10:53PM. This textbook survival guide was created for the textbook: Calculus: Early Transcendental Functions, edition: 6.

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?Differentiation of Vector-Valued Functions In Exercises 1-6, find r’(t), $$\mathrm{r}\left(t_{0}\right)$$, and $$\mathrm{r’}\left(t_{0}\right)$$ for t