(a) If x2 + y2 = 100, find dx (b) Find an equation of the tangent to the circle x² + y² = 100 at the point (6, 8). SOLUTION 1 (a) Differentiating both sides of the equation x? + y? = 100: -(100) dx dx + = 0. Remembering that y is a function of x and using the Chain Rule, we have -(v²) dy dy dx dy dx Thus dy 2x + = 0. dx Now we solve this equation for dy/dx: dy dx (b) At the point (6, 8) we have x = 6 and y = 8, so dy dx An equation of the tangent to the circle at (6, 8) is therefore y (x or
(a) If x2 + y2 = 100, find dx (b) Find an equation of the tangent to the circle x² + y² = 100 at the point (6, 8). SOLUTION 1 (a) Differentiating both sides of the equation x? + y? = 100: -(100) dx dx + = 0. Remembering that y is a function of x and using the Chain Rule, we have -(v²) dy dy dx dy dx Thus dy 2x + = 0. dx Now we solve this equation for dy/dx: dy dx (b) At the point (6, 8) we have x = 6 and y = 8, so dy dx An equation of the tangent to the circle at (6, 8) is therefore y (x or
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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