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 −

4th Edition

ISBN: 9781319323394

Author: Rogawski

Publisher: MAC HIGHER

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

Q6. A fossil piece has been found in Alberta that contains 34% of C14 in it. What is the age of this fossil piece?

Q5. Briefly explain what are isotopes of an elements, with an example, and why some isotopes are radioactive. 470

Q1. Will you earn more interest amount in two years by depositing $2000 in a simple interest account that pays 6% or in an account that pays 6.15% interest compounded monthly? t

Chapter 12 Solutions

CALCULUS W/SAPLING ACCESS >IC<

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