Consider the function f(x) = x + sin(2x) defined on the interval [0, 2x]. Verify that the mean value theorem holds for the function on the given interval. In other words, show that there exists a number € (0, 2) such that (2x)-f(0) 2-0 = f'(5). Round the value of to 2 decimals. Answer:

Linear Algebra: A Modern Introduction
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ISBN:9781285463247
Author:David Poole
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Chapter6: Vector Spaces
Section6.5: The Kernel And Range Of A Linear Transformation
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Consider the function f(x) = x + sin(2x) defined on the interval [0, 2x]. Verify that the mean value theorem holds for the function on the given interval. In other words, show that there exists a number
E € (0, 2) such that
f(2x)-f(0)
2x-0
= f'(§).
Round the value of to 2 decimals.
Answer:
Transcribed Image Text:Consider the function f(x) = x + sin(2x) defined on the interval [0, 2x]. Verify that the mean value theorem holds for the function on the given interval. In other words, show that there exists a number E € (0, 2) such that f(2x)-f(0) 2x-0 = f'(§). Round the value of to 2 decimals. Answer:
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