Explanation Given information: f ( x ) = sin 2 x , a = π 4 and b = 1.1 π 4 . Concept used: Linear approximation: If f is differentiable at x = a and Δ x is small, then - Δ f = f ' ( a ) Δ x Calculation: As per the given information, f ( x ) = sin 2 x , a = π 4 and b = 1.1 π 4 . Δ x = b − a = 1.1 π 4 − π 4 = 0.1 π 4 = π 40 And f ( x ) = sin 2 x ⇒ f ' ( x ) = 2 sin x cos x { Since, d d x ( s i n 2 x ) = 2 sin x cos x } ⇒ f ' ( π 4 ) = 2 sin π 4 cos π 4 ⇒ f ' ( π 4 ) = 2 × 1 2 × 1 2

4th Edition

ISBN: 9781319055905

Author: FRANZOSA

Publisher: VST

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Linear Algebra

In mathematics, problems can be solved by the arithmetic operators like addition, subtraction, multiplication, and division. In algebra, we represent the numbers by any letter called a variable. If these variables are of degree 1, then it is studied unde…

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Question

Chapter 4.1, Problem 23E

To determine

To find the linearization at x=π4 and the value of f(b) using linear approximation.

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Chapter 4.1, Problem 22E

Chapter 4.1, Problem 24E

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Chapter 4 Solutions

EBK CALCULUS: EARLY TRANSCENDENTALS

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To find the linearization at x = π 4 and the value of f ( b ) using linear approximation.

Solution Summary: The author explains how to find the linearization at x=pi 4 and the value of f(b) using linear approximation.

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To find the linearization at x=π4 and the value of f(b) using linear approximation.

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Chapter 4 Solutions