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The Intermediate Value Theorem can be used to approximate a root. The following is an example of binary search in computer science. Suppose you want to approximate v6. You know that it is between 2 and 3. If you consider the function f(x)- Intermediate Value Theorem, there is a value, 2 < c<3 such that f(c) of these two values, 2.5, which is guaranteed to be within 0.5 of the acutal root. f(2.5) will either be less than 0 or greater than 0. You can use the Intermediate Value Theorem again replacing 2.5 with the previous endpoint that has the same sign as 2.5. Continuing this process gives a sequence of approximations r, with e.2.5. How many iterations must you do in order to be within 0.0078125 of the root? 6, then note that f(2) < 0 and f(3)> 0. Therefore by the 0. Next choose the midpoint

The Intermediate Value Theorem can be used to approximate a root. The following is an example of binary search in computer science. Suppose you want to approximate v6. You know that it is between 2 and 3. If you consider the function f(x)- Intermediate Value Theorem, there is a value, 2 < c<3 such that f(c) of these two values, 2.5, which is guaranteed to be within 0.5 of the acutal root. f(2.5) will either be less than 0 or greater than 0. You can use the Intermediate Value Theorem again replacing 2.5 with the previous endpoint that has the same sign as 2.5. Continuing this process gives a sequence of approximations r, with e.2.5. How many iterations must you do in order to be within 0.0078125 of the root? 6, then note that f(2) < 0 and f(3)> 0. Therefore by the 0. Next choose the midpoint

Calculus: Early Transcendentals
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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The Intermediate Value Theorem can be used to approximate a root. The following is an example of binary search in computer science. Suppose you want to approximate v6. You know that it is between 2 and 3. In you consider the function f(@) - x Intermediate Value Theorem, there is a value, 2 < c<3 such that f(c) of these two values, 2.5, which is guaranteed to be within 0.5 of the acutal root. f(2.5) witl efther be less than 0 or greater than 0. You can use the Intermediate Value Theorem again replacing 2.5 with the previous endpoint that has the same sign as 2.5. Continuing this process gives a sequence of approximations , with 6, then note that f(2) < 0 and f(3) > 0. Therefore by the 0. Next choose the midpoint 2.5. How many iterations must you do in order to be within 0.0078125 of the root?
Transcribed Image Text:The Intermediate Value Theorem can be used to approximate a root. The following is an example of binary search in computer science. Suppose you want to approximate v6. You know that it is between 2 and 3. In you consider the function f(@) - x Intermediate Value Theorem, there is a value, 2 < c<3 such that f(c) of these two values, 2.5, which is guaranteed to be within 0.5 of the acutal root. f(2.5) witl efther be less than 0 or greater than 0. You can use the Intermediate Value Theorem again replacing 2.5 with the previous endpoint that has the same sign as 2.5. Continuing this process gives a sequence of approximations , with 6, then note that f(2) < 0 and f(3) > 0. Therefore by the 0. Next choose the midpoint 2.5. How many iterations must you do in order to be within 0.0078125 of the root?
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