a . Explanation Calculation: Consider the expression for the vector r ( t ) . r ( t ) = f ( t ) i + g ( t ) j + h ( t ) k (1) Derive the required constant scalar multiple rule using Equation (1). ∫ a b k r ( t ) d t = ∫ a b [ k f ( t ) i + k g ( t ) j + k h ( t ) k ] d t = ∫ a b [ k f ( t ) ] d t i + ∫ a b [ k g ( t ) ] d t j + ∫ a b [ k h ( t ) ] d b . To determine Establish the given sum and difference rules . c . To determine Establish the given constant vector multiple rules.

Thomas' Calculus: Early Transcendentals Plus Mymathlab With Pearson Etext -- Access Card Package (14th Edition) (hass, Heil & Weir, Thomas' Calculus Series)

14th Edition

ISBN: 9780134665573

Author: Joel R. Hass, Christopher D. Heil, Maurice D. Weir

Publisher: PEARSON

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Question

Chapter 13.2, Problem 43E

To determine

Establish the given constant scalar multiple rule.

To determine

Establish the given sum and difference rules.

To determine

Establish the given constant vector multiple rules.

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Chapter 13.2, Problem 42E

Chapter 13.2, Problem 44E

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Chapter 13 Solutions

Thomas' Calculus: Early Transcendentals Plus Mymathlab With Pearson Etext -- Access Card Package (14th Edition) (hass, Heil & Weir, Thomas' Calculus Series)

Ch. 13.1 - In Exercises 1–4, find the given limits. 1. Ch. 13.1 - In Exercises 1–4, find the given limits. 2. Ch. 13.1 - In Exercises 1–4, find the given limits. 3. Ch. 13.1 - In Exercises 1–4, find the given limits. 4. Ch. 13.1 - Motion in the Plane In Exercises 5–8, r(t) is the...Ch. 13.1 - Motion in the Plane In Exercises 5–8, r(t) is the...Ch. 13.1 - Prob. 7E Ch. 13.1 - Prob. 8E Ch. 13.1 - Prob. 9E Ch. 13.1 - Prob. 10E

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