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3. Given an equation I In r= 1. - 1. a). Use the IVT (Intermediate Value Theorem) to show that the equation has a solution. b). Use a graphing utility to find all the solution(s) to the equation, to verify a).

3. Given an equation I In r= 1. - 1. a). Use the IVT (Intermediate Value Theorem) to show that the equation has a solution. b). Use a graphing utility to find all the solution(s) to the equation, to verify a).

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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3. Given an equation r In r 1. a). Use the IVT (Intermnediate Value Theorem) to show that the equation has a solution. b). Use a graphing utility to find all the solution(s) to the equation, to verify a). [Hint: Find f (x) such that f (x) = 0 is equivalent to the given equation.]
Transcribed Image Text:3. Given an equation r In r 1. a). Use the IVT (Intermnediate Value Theorem) to show that the equation has a solution. b). Use a graphing utility to find all the solution(s) to the equation, to verify a). [Hint: Find f (x) such that f (x) = 0 is equivalent to the given equation.]
Expert Solution
Step 1

We have to use the intermediate value theorem to show that the equation xlnx=1 has

a solution. Let fx=xlnx-1. Then we have to show that there exists x0 such that

fx0=0.

Intermediate value theorem: If fx is a continuous function on any interval a, b and

f has opposite signs inside this interval, then there exists c∈a, b such that fc=0.

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