he Intermediate Value Theorem can be used to approximate a root. The following is an example of binary earch in computer science. Suppose you want to approximate √5. You know that it is between 2 and 3. If you onsider the function f(x)=x²-5, then note that f(2) < 0 and f(3) > 0. Therefore by the Intermediate alue Theorem, there is a value, 2 ≤ c < 3 such that f(c) 0. Next choose the midpoint of these two alues, 2.5, which is guaranteed to be within 0.5 of the acutal root. f(2.5) will either be less than 0 or reater 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 en with 1 = 2.5. low many iterations must you do in order to be within 0.00390625 of the root? Submit Question Jump to Answer =
he Intermediate Value Theorem can be used to approximate a root. The following is an example of binary earch in computer science. Suppose you want to approximate √5. You know that it is between 2 and 3. If you onsider the function f(x)=x²-5, then note that f(2) < 0 and f(3) > 0. Therefore by the Intermediate alue Theorem, there is a value, 2 ≤ c < 3 such that f(c) 0. Next choose the midpoint of these two alues, 2.5, which is guaranteed to be within 0.5 of the acutal root. f(2.5) will either be less than 0 or reater 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 en with 1 = 2.5. low many iterations must you do in order to be within 0.00390625 of the root? Submit Question Jump to Answer =
College Algebra (MindTap Course List)
12th Edition
ISBN:9781305652231
Author:R. David Gustafson, Jeff Hughes
Publisher:R. David Gustafson, Jeff Hughes
Chapter4: Polynomial And Rational Functions
Section4.5: Zeros Of Polynomial Functions
Problem 79E
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![Question 11
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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 √5. You know that it is between 2 and 3. If you
consider the function f(x)=x²-5, then note that f(2) < 0 and f(3) > 0. Therefore by the Intermediate
Value Theorem, there is a value, 2 ≤ c < 3 such that f(c) = 0. Next choose the midpoint 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 with 1 = 2.5.
How many iterations must you do in order to be within 0.00390625 of the root?
Jump to Answer](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fbf32ca19-f396-4c66-88b1-2ce5311e0ec6%2F8cb99d8b-41a4-41af-a5ad-26bb43548b37%2Fs6kubf_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Question 11
Textbook
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Submit Question
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Videos [+]
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 √5. You know that it is between 2 and 3. If you
consider the function f(x)=x²-5, then note that f(2) < 0 and f(3) > 0. Therefore by the Intermediate
Value Theorem, there is a value, 2 ≤ c < 3 such that f(c) = 0. Next choose the midpoint 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 with 1 = 2.5.
How many iterations must you do in order to be within 0.00390625 of the root?
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