If ๐‘“(๐‘ฅ) = ๐‘ ๐‘–๐‘›โˆ’1๐‘ฅ, 0 < ๐‘Ž < ๐‘ < 1, use Mean value theorem to prove that๐‘ โˆ’ ๐‘Žโˆš1 โˆ’ ๐‘Ž2 < ๐‘ ๐‘–๐‘›โˆ’1๐‘ โˆ’ ๐‘ ๐‘–๐‘›โˆ’1๐‘Ž < ๐‘ โˆ’ ๐‘Žโˆš1 โˆ’ ๐‘2

Question

If ๐‘“(๐‘ฅ) = ๐‘ ๐‘–๐‘›โˆ’1๐‘ฅ, 0 < ๐‘Ž < ๐‘ < 1, use Mean value theorem to prove that๐‘ โˆ’ ๐‘Žโˆš1 โˆ’ ๐‘Ž2 < ๐‘ ๐‘–๐‘›โˆ’1๐‘ โˆ’ ๐‘ ๐‘–๐‘›โˆ’1๐‘Ž < ๐‘ โˆ’ ๐‘Žโˆš1 โˆ’ ๐‘2
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Solution 1

The Mean Value Theorem (MVT) states that if a function f is continuous on the closed interval [a, b] and differentiable on the open interval (a, b), then there exists at least one number c in the interval (a, b) such that the derivative of the function at that point is equal to the average rate of c Knowee AI StudyGPT is a powerful AI-powered study tool designed to help you to solve study prob

Knowee AI StudyGPT is a powerful AI-powered study tool designed to help you to solve study problem.
Knowee AI StudyGPT is a powerful AI-powered study tool designed to help you to solve study problem.
Knowee AI StudyGPT is a powerful AI-powered study tool designed to help you to solve study problem.
Knowee AI StudyGPT is a powerful AI-powered study tool designed to help you to solv

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If ๐‘“(๐‘ฅ) = ๐‘ ๐‘–๐‘›โˆ’1๐‘ฅ, 0 < ๐‘Ž < ๐‘ < 1, use Mean value theorem to prove that๐‘ โˆ’ ๐‘Žโˆš1 โˆ’ ๐‘Ž2 < ๐‘ ๐‘–๐‘›โˆ’1๐‘ โˆ’ ๐‘ ๐‘–๐‘›โˆ’1๐‘Ž < ๐‘ โˆ’ ๐‘Žโˆš1 โˆ’ ๐‘2

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