Use the Intermediate Value Theorem to show that there is a root of the given equation in the specified interval. ex = 5 - 4x, (0, 1) The equation ex = 5 - 4x is equivalent to the equation f(x) = ex - 5 + 4x = 0. f(x) is continuous on the interval [0, 1], f(0) = , and f(1) = Since V ---Select--- <0 < ---Select- , 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 ex = 5 - 4x, in the interval (0, 1). f(0) f(1)

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter4: Polynomial And Rational Functions
Section: Chapter Questions
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Use the Intermediate Value Theorem to show that there is a root of the given equation in the specified interval.
ex = 5 – 4x, (0, 1)
The equation ex
= 5
4x is equivalent to the equation f(x) = ex – 5 + 4x
= 0. f(x) is continuous on the interval [0, 1], f(0) =
and f(1)
Since
V ---Select---
---Select---
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 e* = 5 – 4x, in the interval (0, 1).
f(0)
f(1)
Transcribed Image Text:Use the Intermediate Value Theorem to show that there is a root of the given equation in the specified interval. ex = 5 – 4x, (0, 1) The equation ex = 5 4x is equivalent to the equation f(x) = ex – 5 + 4x = 0. f(x) is continuous on the interval [0, 1], f(0) = and f(1) Since V ---Select--- ---Select--- 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 e* = 5 – 4x, in the interval (0, 1). f(0) f(1)
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