A graphing calculator is recommended.Consider the following.cos(x) = x3(a) Prove that the equation has at least one real solution.The equation cos(x) = x° is equivalent to the equation f(x) = cos(x) – x = 0. f(x) is continuous on the interval [0, 1], f(0) = 1and f(1) = -0.4596976941Since f(1)<0< f(0)V , there is a number c in(0, 1) such that f(c) = 0 by the Intermediate Value Theorem. Thus, there is a root of the equation cos(x) = x, in the interval (0, 1).(b) Use a calculator to find an interval of length 0.01 that contains a solution. (Enter your answer using interval notation. Round your answers to two decimal places.)(0.86, 0.87)

Answered: Image /qna-images/answer/c2e8e3d5-ffaf-41b7-aa7d-9a2f56931193.jpg

A graphing calculator is recommended. Consider the following. cos(x) = x3 (a) Prove that the equation has at least one real solution. The equation cos(x) = x is equivalent to the equation f(x) = cos(x) - x* = 0. f(x) is continuous on the interval [0, 1), f(0) = 1 and f(1) = -0.4596976941 Since f1) vv <0< (0) , there is a number c in (0, 1) such that f(c) = 0 by the Intermediate Value Theorem. Thus, there is a root of the equation cos(x) = x, in the interval (0, 1). (b) Use a calculator to find an interval of length 0.01 that contains a solution. (Enter your answer using interval notation. Round your answers to two decimal places.) (0.86, 0.87)

A graphing calculator is recommended. Consider the following. cos(x) = x3 (a) Prove that the equation has at least one real solution. The equation cos(x) = x is equivalent to the equation f(x) = cos(x) - x* = 0. f(x) is continuous on the interval [0, 1), f(0) = 1 and f(1) = -0.4596976941 Since f1) vv <0< (0) , there is a number c in (0, 1) such that f(c) = 0 by the Intermediate Value Theorem. Thus, there is a root of the equation cos(x) = x, in the interval (0, 1). (b) Use a calculator to find an interval of length 0.01 that contains a solution. (Enter your answer using interval notation. Round your answers to two decimal places.) (0.86, 0.87)

Functions and Change: A Modeling Approach to College Algebra (MindTap Course List)

6th Edition

ISBN:9781337111348

Author:Bruce Crauder, Benny Evans, Alan Noell

Publisher:Bruce Crauder, Benny Evans, Alan Noell

Chapter2: Graphical And Tabular Analysis

Section2.1: Tables And Trends

Problem 1TU: If a coffee filter is dropped, its velocity after t seconds is given by v(t)=4(10.0003t) feet per...

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Question

A graphing calculator is recommended.
Consider the following.
cos(x) = x3
(a) Prove that the equation has at least one real solution.
The equation cos(x) = x° is equivalent to the equation f(x) = cos(x) – x = 0. f(x) is continuous on the interval [0, 1], f(0) = 1
and f(1) = -0.4596976941
Since f(1)
<0< f(0)
V , there is a number c in
(0, 1) such that f(c) = 0 by the Intermediate Value Theorem. Thus, there is a root of the equation cos(x) = x, in the interval (0, 1).
(b) Use a calculator to find an interval of length 0.01 that contains a solution. (Enter your answer using interval notation. Round your answers to two decimal places.)
(0.86, 0.87)

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