Use the intermediate value theorem to prove that the functions y = cos(x) and y = x intersect at a value in the interval [0, 1]. Note: You are not being asked to find the value. Hint: Solve for 0 on one side of the following equation first and use the intermediate value theorem to find the root. cos(x) = = x

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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2) Use the intermediate value theorem to prove that the functions y cos(x) and y = x intersect
at a value in the interval [0, 1]. Note: You are not being asked to find the value. Hint: Solve for 0
on one side of the following equation first and use the intermediate value theorem to find the root.
cos(x) = = X
Transcribed Image Text:= 2) Use the intermediate value theorem to prove that the functions y cos(x) and y = x intersect at a value in the interval [0, 1]. Note: You are not being asked to find the value. Hint: Solve for 0 on one side of the following equation first and use the intermediate value theorem to find the root. cos(x) = = X
Expert Solution
Step 1

Proof:

To use the intermediate value theorem, we need to show that the function f(x) = cos(x) - x has opposite signs at the endpoints of the interval [0, 1].

 

 

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