Explanation Given: c ( t ) = ( e − t cos t , e − t sin t ) for 0 ≤ t < ∞ . Formula Used: The length of a curve c ( t ) from t = a to t = b will be given by: L = ∫ t = a t = b ( d x d t ) 2 + ( d y d t ) 2 d t Calculation: It is given that c ( t ) = ( e − t cos t , e − t sin t ) that means we have x ( t ) = e − t cos t , y ( t ) = e − t sin t . Now, differentiate both the equations x ( t ) = e − t cos t , y ( t ) = e − t sin t with respect to t and we get: x ( t ) = e − t cos t , y ( t ) = e − t sin t d x d t = − e − t ( cos t + sin t ) , d y d t = e − t ( cos t − sin t ) So, ( d x d t ) 2 + ( d y d t ) 2 = ( − e − t ( cos t + sin t ) ) 2 + ( e − t ( cos t −

3rd Edition

ISBN: 9781464125263

Author: Jon Rogawski, Colin Adams

Publisher: W.H. Freeman & Co

See similar textbooks

Concept explainers

Linear Algebra

In mathematics, problems can be solved by the arithmetic operators like addition, subtraction, multiplication, and division. In algebra, we represent the numbers by any letter called a variable. If these variables are of degree 1, then it is studied unde…

Videos

Question

Chapter 12, Problem 23CRE

To determine

That $c (t)$ for $0 \leq t < \infty$ has finite length and to determine its length

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 12, Problem 22CRE

Chapter 12, Problem 24CRE

Students have asked these similar questions

Please refer below

For the following function f and real number a, a. find the slope of the tangent line mtan = f' (a), and b. find the equation of the tangent line to f at x = a. f(x)= 2 = a = 2 x2 a. Slope: b. Equation of tangent line: y

Please refer below

Chapter 12 Solutions

Calculus - Standalone book

Ch. 12.1 - Prob. 1PQ Ch. 12.1 - Prob. 2PQ Ch. 12.1 - Prob. 3PQ Ch. 12.1 - Prob. 4PQ Ch. 12.1 - Prob. 5PQ Ch. 12.1 - Prob. 6PQ Ch. 12.1 - Prob. 7PQ Ch. 12.1 - Prob. 1E Ch. 12.1 - Prob. 2E Ch. 12.1 - Prob. 3E

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.

That c ( t ) for 0 ≤ t < ∞ has finite length and to determine its length

Solution Summary: The author explains that c (t) for 0 t has finite length and determines its length by comparing the equations x, y, and d.

Concept explainers

Videos

That $c (t)$ for $0 \leq t < \infty$ has finite length and to determine its length

Want to see the full answer?

Chapter 12 Solutions

That c ( t ) for 0 ≤ t &lt; ∞ has finite length and to determine its length

Solution Summary: The author explains that c (t) for 0 t has finite length and determines its length by comparing the equations x, y, and d.

Concept explainers

Videos

That c(t) for 0≤t<∞ has finite length and to determine its length

Want to see the full answer?

Chapter 12 Solutions

That c ( t ) for 0 ≤ t < ∞ has finite length and to determine its length

That $c (t)$ for $0 \leq t < \infty$ has finite length and to determine its length