Explanation Given: The function is 2.1 − 2 or 9.1 − 9 . Formula used: Linear approximation of Δ f : If f is differentiable at x = a and Δ x is small then Δ f ≈ f ′ ( a ) Δ x Where Δ f = f ( a + Δ x ) − f ( a ) . Calculation: Consider the function f ( x ) = x . Differentiate the function with respect to x . f ′ ( x ) = 1 2 x Find the value of 2.1 − 2 . Now, apply the linear approximation with a = 2 and Δ x = 0.1 . Use the formula: f ′ ( a ) ( Δ x ) = f ( a + Δ x ) − f ( a ) f ′ ( 2 ) ( 0.1 ) = f ( 2 + 0.1 ) − f ( 2 ) ( 1 2 2 ) ( 0.1 ) = 2.1 − 2 0

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ISBN: 9781319050733

Author: Rogawski

Publisher: MAC HIGHER

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Question

Chapter 4.1, Problem 33E

To determine

Find which is larger using linear approximation: 2.1−2 or 9.1−9 ?

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Chapter 4.1, Problem 32E

Chapter 4.1, Problem 34E

Chapter 4 Solutions

CALCULUS (CLOTH)

Ch. 4.1 - Prob. 1PQ Ch. 4.1 - Prob. 2PQ Ch. 4.1 - Prob. 3PQ Ch. 4.1 - Prob. 4PQ Ch. 4.1 - Prob. 1E Ch. 4.1 - Prob. 2E Ch. 4.1 - Prob. 3E Ch. 4.1 - Prob. 4E Ch. 4.1 - Prob. 5E Ch. 4.1 - Prob. 6E

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Find which is larger using linear approximation: 2.1 − 2 or 9.1 − 9 ?

Solution Summary: The author explains the linear approximation of the value of sqrt2.

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Find which is larger using linear approximation: 2.1−2 or 9.1−9 ?

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Chapter 4 Solutions