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(a) Sketch y = secx on a restricted domain of length 7 where the function is one-to- one. Choose such a domain with angles in Quadrants 1 and 2 only. (b) Sketch a graph of the inverse secant function defined using this domain restriction. Give the domain and range of the inverse secant according to this definition. (c) Give the open intervals where the arcsecant is increasing or decreasing. What does this tell you about the derivative of the inverse secant? 1 (d) Show that dy de |x|√x²- =

(a) Sketch y = secx on a restricted domain of length 7 where the function is one-to- one. Choose such a domain with angles in Quadrants 1 and 2 only. (b) Sketch a graph of the inverse secant function defined using this domain restriction. Give the domain and range of the inverse secant according to this definition. (c) Give the open intervals where the arcsecant is increasing or decreasing. What does this tell you about the derivative of the inverse secant? 1 (d) Show that dy de |x|√x²- =

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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Derivative of inverse tangent Can you do 33
Theorem 11 (Derivative of the Inverse Tangent) d dx 31. (a) Sketch an accurate graph of the cosine on the domain (-27, 27). Use this to sketch an accurate graph of the secant function on the same set of axes. (b) Identify at least three domains of length 7 where the secant is one-to-one. 32. (a) Sketch y = secx on a restricted domain of length where the function is one-to- one. Choose such a domain with angles in Quadrants 1 and 3 only. (b) Sketch a graph of the inverse secant function defined using this domain restriction. (c) Give the domain and range of the inverse secant according to this definition. (d) Give the open intervals where the inverse secant is increasing or decreasing. What does this tell you about the derivative of the inverse secant? 1 (e) Show that dy dr x√x² - 1 33. (a) Sketch y = secx on a restricted domain of length 7 where the function is one-to- one. Choose such a domain with angles in Quadrants 1 and 2 only. FOL = (b) Sketch a graph of the inverse secant function defined using this domain restriction. Give the domain and range of the inverse secant according to this definition. arctan r (c) Give the open intervals where the arcsecant is increasing or decreasing. What does this tell you about the derivative of the inverse secant? 1 (d) Show that |x|√x² - I' dy de ID LA CAL
Transcribed Image Text:Theorem 11 (Derivative of the Inverse Tangent) d dx 31. (a) Sketch an accurate graph of the cosine on the domain (-27, 27). Use this to sketch an accurate graph of the secant function on the same set of axes. (b) Identify at least three domains of length 7 where the secant is one-to-one. 32. (a) Sketch y = secx on a restricted domain of length where the function is one-to- one. Choose such a domain with angles in Quadrants 1 and 3 only. (b) Sketch a graph of the inverse secant function defined using this domain restriction. (c) Give the domain and range of the inverse secant according to this definition. (d) Give the open intervals where the inverse secant is increasing or decreasing. What does this tell you about the derivative of the inverse secant? 1 (e) Show that dy dr x√x² - 1 33. (a) Sketch y = secx on a restricted domain of length 7 where the function is one-to- one. Choose such a domain with angles in Quadrants 1 and 2 only. FOL = (b) Sketch a graph of the inverse secant function defined using this domain restriction. Give the domain and range of the inverse secant according to this definition. arctan r (c) Give the open intervals where the arcsecant is increasing or decreasing. What does this tell you about the derivative of the inverse secant? 1 (d) Show that |x|√x² - I' dy de ID LA CAL
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