Explanation Given Info: Given position vector r ( t ) = 〈 3 + 4 t , 3 − 5 t , 9 t 〉 . Formula Used: The unit tangent vector is T ( t ) = r ' ( t ) | r ' ( t ) | . Calculation: r ' ( t ) = d r ( t ) d t r ' ( t ) = d 〈 3 + 4 t , 3 − 5 t , 9 t 〉 d t r ' ( t ) = 〈 4 , − 5 , 9 〉 | r ' ( t ) | = 4 2 + 5 2

4th Edition

ISBN: 9781319434540

Author: Rogawski

Publisher: MAC HIGHER

See similar textbooks

Concept explainers

Optimization

Optimization comes from the same root as "optimal". "Optimal" means the highest. When you do the optimization process, that is when you are "making it best" to maximize everything and to achieve optimal results, a set of parameters is the base for the se…

Integration

Integration means to sum the things. In mathematics, it is the branch of Calculus which is used to find the area under the curve. The operation subtraction is the inverse of addition, division is the inverse of multiplication. In the same way, integratio…

Application of Integration

In mathematics, the process of integration is used to compute complex area related problems. With the application of integration, solving area related problems, whether they are a curve, or a curve between lines, can be done easily.

Volume

In mathematics, we describe the term volume as a quantity that can express the total space that an object occupies at any point in time. Usually, volumes can only be calculated for 3-dimensional objects. By 3-dimensional or 3D objects, we mean objects th…

Area

Area refers to the amount of space a figure encloses and the number of square units that cover a shape. It is two-dimensional and is measured in square units.

Videos

Question

Chapter 14.4, Problem 3E

To determine

$r' (t)$ and $T (t)$ . Evaluate $T (1)$ .

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 14.4, Problem 2E

Chapter 14.4, Problem 4E

Students have asked these similar questions

The graph of f' is below. Use it to determine where the local minima and maxima for f are. If there are multiple answers, separate with commas. 2 f'(x) N -5 -4 3-2-1 -1 -2 -3 -4 12 3 4 5 -x Local minima at x Local maxima at x

The graph of f' is below. Use it to determine the intervals where f is increasing. -5-4-32 4- 3 2 1 -2 -3 +x 2 3 4 5

The graph of f' is below. Use it to determine where the inflection points are and the intervals where f is concave up and concave down. If there are multiple inflection points, separate with a comma. 6 5 4 3 2 1 f'(x) +x -6-5-4-3 -2 -1 1 2 3 4 5 6 -1 -2 -3 -4 -5 -6+ Inflection point(s) at x = Concave up: Concave down:

Chapter 14 Solutions

ACHIEVE STANDALONE ACCESS F/ CALC 4E

Ch. 14.1 - Prob. 1PQ Ch. 14.1 - Prob. 2PQ Ch. 14.1 - Prob. 3PQ Ch. 14.1 - Prob. 4PQ Ch. 14.1 - Prob. 5PQ Ch. 14.1 - Prob. 6PQ Ch. 14.1 - Prob. 1E Ch. 14.1 - Prob. 2E Ch. 14.1 - Prob. 3E Ch. 14.1 - Prob. 4E

Knowledge Booster

$Calculus$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, calculus and related others by exploring similar questions and additional content below.

r ' ( t ) and T ( t ) . Evaluate T ( 1 ) .

Solution Summary: The author explains that the unit tangent vector is T ( t ) = r'(t) and d .

Concept explainers

Videos

$r' (t)$ and $T (t)$ . Evaluate $T (1)$ .

Want to see the full answer?

Chapter 14 Solutions

r ' ( t ) and T ( t ) . Evaluate T ( 1 ) .

Solution Summary: The author explains that the unit tangent vector is T ( t ) = r'(t) and d .

Concept explainers

Videos

r'(t) and T(t). Evaluate T(1).

Want to see the full answer?

Chapter 14 Solutions

$r' (t)$ and $T (t)$ . Evaluate $T (1)$ .