Consider the following. cos(x) = x3 (a) Prove that the equation has at least one real root. The equation cos(x) = x³ is equivalent to the equation f(x) = cos(x) – x³ = 0. f(x) is continuous on the interval [0, 1], f(0) = , and f(1) = . Since ---Select--- ♥ < 0 < ---Select--- 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) = x³, in the interval (0, 1). (b) Use your calculator to find an interval of length 0.01 that contains a root. (Enter your answer using interval notation. Round your answers to two decimal places.)

Consider the following. cos(x) = x3 (a) Prove that the equation has at least one real root. The equation cos(x) = x³ is equivalent to the equation f(x) = cos(x) – x³ = 0. f(x) is continuous on the interval [0, 1], f(0) = , and f(1) = . Since ---Select--- ♥ < 0 < ---Select--- 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) = x³, in the interval (0, 1). (b) Use your calculator to find an interval of length 0.01 that contains a root. (Enter your answer using interval notation. Round your answers to two decimal places.)

Calculus For The Life Sciences

2nd Edition

ISBN:9780321964038

Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Chapter4: Calculating The Derivative

Section4.2: Derivatives Of Products And Quotients

Problem 35E

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