1. In this problem you will prove that the shortest distance between two points is a line using the calculus of variations. Consider a curve y(x) whose endpoints are fixed: y(x = 0) = 0, y(x = d) = h. (1) That is, the curve goes from (0,0) to (d, h). (a) Write an integral expression for the arc length l of the curve in terms of the function y(x). Your expression should have the form = | dxo(y(x),y'(x)). (2) Determine the function o. Hint: Use the fact that the infinitesmal distance ds between two Vdx? + dy?. Write this in terms of dr points (x, y) and (x + dx, y + dy) is given by ds and the function y(x).

1. In this problem you will prove that the shortest distance between two points is a line using the calculus of variations. Consider a curve y(x) whose endpoints are fixed: y(x = 0) = 0, y(x = d) = h. (1) That is, the curve goes from (0,0) to (d, h). (a) Write an integral expression for the arc length l of the curve in terms of the function y(x). Your expression should have the form = | dxo(y(x),y'(x)). (2) Determine the function o. Hint: Use the fact that the infinitesmal distance ds between two Vdx? + dy?. Write this in terms of dr points (x, y) and (x + dx, y + dy) is given by ds and the function y(x).

Calculus: Early Transcendentals

8th Edition

ISBN:9781285741550

Author:James Stewart

Publisher:James Stewart

Chapter1: Functions And Models

Section: Chapter Questions

Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...

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