a. Explanation Given: The expression 1 + h and h is very small. Formula used: The formula for binomial expansion states that if | x | < 1 , and n is positive or negative integer or fraction then ( 1 + x ) n = 1 + n 1 ! x + n ( n − 1 ) 2 ! x 2 + n ( n − 1 ) ( n − 2 ) 3 ! x 3 ⋯ n ( n − 1 ) ( n − 2 ) ⋯ ( n − r + 1 ) r ! x r ⋯ ∞ Calculation: The given expression can be written as ( 1 + h ) 1 2 . Therefore, from the binomial expansion ( 1 + h ) 1 2 ( 1 + h ) 1 2 = 1 + 1 2 1 ! b. To determine To show: That if h is very small 1 1 + h is approximately equal to 1 − h

7th Edition

ISBN: 9781524916817

Author: SMITH KARL J, STRAUSS MONTY J, TODA MAGDALENA DANIELE

Publisher: Kendall Hunt Publishing

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Differential Equations

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Chapter 3.8, Problem 55PS

To determine

To show:That if h is very small 1+h is approximately equal to 1+h2

To determine

To show:That if h is very small 11+h is approximately equal to 1−h

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Chapter 3.8, Problem 53PS

Chapter 3.8, Problem 56PS

Chapter 3 Solutions

Calculus

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That if h is very small 1 + h is approximately equal to 1 + h 2

Solution Summary: The author shows that if h is very small, sqrt1+h is approximately equal to 1+

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To show:That if h is very small 1+h is approximately equal to 1+h2

To show:That if h is very small 11+h is approximately equal to 1−h

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Chapter 3 Solutions