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1. Find the rate of change of the area of a circle with respect to its radius when the radius is 3 feet. of change of y with respect to x

1. Find the rate of change of the area of a circle with respect to its radius when the radius is 3 feet. of change of y with respect to x

Calculus: Early Transcendentals
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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III. Solve the following problems. Use only Four-step Rule 1. Find the rate of change of the area of a circle with respect to its radius when the radius is 3 feet. 2. For the function y = xVx find the value of x for which the rate of change of y with respect to x is 6. 3. Find the rate at which the volume of a right circular cylinder of constant altitude 10 feet changes with respect to its diameter when the radius is 5 feet.
Transcribed Image Text:III. Solve the following problems. Use only Four-step Rule 1. Find the rate of change of the area of a circle with respect to its radius when the radius is 3 feet. 2. For the function y = xVx find the value of x for which the rate of change of y with respect to x is 6. 3. Find the rate at which the volume of a right circular cylinder of constant altitude 10 feet changes with respect to its diameter when the radius is 5 feet.
JYIDUIS Used to denote the derivative are D,y , D,f(x) , y', f'(x) ,- f(x) The process of finding when y = f(x) is known, is called differentiation ; and if the deriva xp exists, f(x) is said to be a differentiable function. FOUR-STEP RULE 1. Substitute x + Ax for x and y+Ay for y in y=f(x). 2. Subtract y=f(x) from the result of step 1 to obtain Ay in terms of x and Ax 3. Divide both sides of the result of step 2 by Ax 4. Find the limit of the result of step 3 as Ax approaches zero.
Transcribed Image Text:JYIDUIS Used to denote the derivative are D,y , D,f(x) , y', f'(x) ,- f(x) The process of finding when y = f(x) is known, is called differentiation ; and if the deriva xp exists, f(x) is said to be a differentiable function. FOUR-STEP RULE 1. Substitute x + Ax for x and y+Ay for y in y=f(x). 2. Subtract y=f(x) from the result of step 1 to obtain Ay in terms of x and Ax 3. Divide both sides of the result of step 2 by Ax 4. Find the limit of the result of step 3 as Ax approaches zero.
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