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use implicit differentiction to find an equation of the tangent line to the graph of arctan (x+y) = y°+ at (1,0). 4 write the equation of tHe tengont line in slope -intercept form.

use implicit differentiction to find an equation of the tangent line to the graph of arctan (x+y) = y°+ at (1,0). 4 write the equation of tHe tengont line in slope -intercept form.

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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**Finding the Tangent Line using Implicit Differentiation** **Problem Statement:** Use implicit differentiation to find an equation of the tangent line to the graph of arctan(x + y) = y^2 + π/4 at (1, 0). Write the equation of the tangent line in slope-intercept form. --- To solve the problem of finding the tangent line to the given function at the specified point, the following steps should be undertaken: 1. Apply implicit differentiation to both sides of the equation with respect to x. 2. Solve for dy/dx (the slope of the tangent line). 3. Evaluate the derivative at the given point (1, 0) to find the specific slope. 4. Use the point-slope equation of a line to determine the tangent line in slope-intercept form. Follow the above steps to fully understand and solve the problem effectively. A detailed explanation with appropriate calculations and step-by-step solving techniques would likely be provided on the educational website to aid in comprehension. The goal is to ensure students can replicate the process for similar problems involving implicit differentiation and finding tangent lines.
Transcribed Image Text:**Finding the Tangent Line using Implicit Differentiation** **Problem Statement:** Use implicit differentiation to find an equation of the tangent line to the graph of arctan(x + y) = y^2 + π/4 at (1, 0). Write the equation of the tangent line in slope-intercept form. --- To solve the problem of finding the tangent line to the given function at the specified point, the following steps should be undertaken: 1. Apply implicit differentiation to both sides of the equation with respect to x. 2. Solve for dy/dx (the slope of the tangent line). 3. Evaluate the derivative at the given point (1, 0) to find the specific slope. 4. Use the point-slope equation of a line to determine the tangent line in slope-intercept form. Follow the above steps to fully understand and solve the problem effectively. A detailed explanation with appropriate calculations and step-by-step solving techniques would likely be provided on the educational website to aid in comprehension. The goal is to ensure students can replicate the process for similar problems involving implicit differentiation and finding tangent lines.
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