Explanation Given information: An expression is given as, ( 3.1 2 ) sin ( 3.1 2 ) . Concept used: Linear approximation: If f is differentiable at x = a and Δ x is small, then - Δ f = f ' ( a ) Δ x Calculation: An expression is given as, ( 3.1 2 ) sin ( 3.1 2 ) . Let us suppose, f ( x ) = x 2 sin ( x 2 ) and a = 3 , b = 3.1 . We use the linearization of f ( x ) = x 2 sin ( x 2 ) at a = 3 in approximation. ∴ Δ x = b − a = 3.1 − 3 = 0.1 . f ( x ) = x 2 sin ( x 2 ) ⇒ f ( x ) = 1 2 x csc ( x 2 ) ⇒ f ' ( x ) = 1 2 [ x ⋅ ( − 1 2 csc x 2 cot x 2 ) + csc ( x 2 ) ⋅ 1 ] { Using product rule, d ( u v ) d x = u d v d x + v d u d x } ⇒ f ' ( x ) = − 1 4 csc

4th Edition

ISBN: 9781319323394

Author: Rogawski

Publisher: MAC HIGHER

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Chapter 4.1, Problem 63E

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The value of ( 3.12)sin( 3.12) using linear approximation.

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Chapter 4.1, Problem 62E

Chapter 4.1, Problem 64E

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The value of ( 3.1 2 ) sin ( 3.1 2 ) using linear approximation.

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The value of ( 3.12)sin( 3.12) using linear approximation.

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Chapter 4 Solutions