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x² + y² = 25 at (4, -3)

x² + y² = 25 at (4, -3)

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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implicit differentiation. 1. Find an equation for the tangent line to the graph of the given equation at the specified point. You will need to use A. x² + y² = 25 at (4, -3) B. x² + 3xy - 5y² = 5 at (2, 1) C. xy² +y: = 14 at (3,2) 2. Consider a circle that is expanding in size with time t in seconds. Use the area of a circle equation A = problem. A. You are told that the radius is increasing at a rate of 3 cm/s. Find the rate of change of the area A (measured in cm^2) with respect to time t (measured in s) at the moment when r = 3 cm. B. You are now instead told that the area is increasing at a rate of 3 cm^2/s. Find the rate of change of the radius r (measured in cm) with respect to time t (measured in s) at the moment when r = 3 cm. 3. A 13 ft ladder is sliding down a wall as depicted below. Use the Pythagorean Theorem x². + y² = 13² for this problem. 50 ladder 13 St Tr² for this x A. You are told that at this very moment the bottom of the ladder is 5 ft from the wall and is sliding away from the wall at 2 ft/min. Find the rate at which the top of the ladder is sliding down the wall. B. You are instead told that at this very moment the top of the ladder is 5 ft above the ground and is sliding down the the wall at a rate of -3 ft/min. Find the rate at which the bottom of the ladder is sliding away from the wall.
Transcribed Image Text:implicit differentiation. 1. Find an equation for the tangent line to the graph of the given equation at the specified point. You will need to use A. x² + y² = 25 at (4, -3) B. x² + 3xy - 5y² = 5 at (2, 1) C. xy² +y: = 14 at (3,2) 2. Consider a circle that is expanding in size with time t in seconds. Use the area of a circle equation A = problem. A. You are told that the radius is increasing at a rate of 3 cm/s. Find the rate of change of the area A (measured in cm^2) with respect to time t (measured in s) at the moment when r = 3 cm. B. You are now instead told that the area is increasing at a rate of 3 cm^2/s. Find the rate of change of the radius r (measured in cm) with respect to time t (measured in s) at the moment when r = 3 cm. 3. A 13 ft ladder is sliding down a wall as depicted below. Use the Pythagorean Theorem x². + y² = 13² for this problem. 50 ladder 13 St Tr² for this x A. You are told that at this very moment the bottom of the ladder is 5 ft from the wall and is sliding away from the wall at 2 ft/min. Find the rate at which the top of the ladder is sliding down the wall. B. You are instead told that at this very moment the top of the ladder is 5 ft above the ground and is sliding down the the wall at a rate of -3 ft/min. Find the rate at which the bottom of the ladder is sliding away from the wall.
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