(a)
To find: Theidentification sign of the second term for each expansion.
(a)
Answer to Problem 2CFU
By observing the above three expansions, the sign of the second term of each expansion is negative.
Explanation of Solution
Given:
Concept used:
Binomial expansion:
Calculation:
First, find the expansion of
Substitute
By using the above formula:
By putting the value from the given:
Therefore, the equation can be written as:
In this expansion, first and third terms are positive but second and fourth terms are negative.
Similarly,
For
Hence, by observing the above three expansions, the sign of the second term of each expansion is negative.
(b)
To find:the identification the sign of the third term for the expansion.
(b)
Answer to Problem 2CFU
By observing the above three expansions, the sign of the third term of each expansion is positive.
Explanation of Solution
Given:
Concept used:
Binomial expansion:
Calculation:
First, find the expansion of
Substitute
By using the above formula:
By putting the value from the given:
Therefore, the equation can be written as:
In this expansion, first and third terms are positive but second and fourth terms are negative.
Similarly,
For
Hence, by observing the above three expansions, the sign of the third term of each expansion is positive.
(c)
To find:the explanation to determine the sign of a term without writing out the entire expansion.
(c)
Answer to Problem 2CFU
Using the mentioned statements, it can decide the sign of the term in the expansions.
Explanation of Solution
Given:
Concept used:
Binomial expansion:
Calculation:
Here it can be clearly observed that the sign of first term is positive and the sign of the second term is negative in the three binomials.
Particularly, the sign of the terms in the expansion depends upon the exponent of second term only because, second term is negative and the first term is positive.
If the exponent of second term is an even number, then the sign is positive.
And if the exponent of the second term is an odd number, then the sign is negative.
But an exponent of first term is either positive or negative, the sign is positive.
Hence, by using thementioned statements, it can decide the sign of the term in the expansions.
Chapter 12 Solutions
Advanced Mathematical Concepts: Precalculus with Applications, Student Edition
Additional Math Textbook Solutions
Thomas' Calculus: Early Transcendentals (14th Edition)
Calculus and Its Applications (11th Edition)
Calculus: Early Transcendentals (3rd Edition)
Precalculus
Calculus: Early Transcendentals (2nd Edition)
University Calculus: Early Transcendentals (3rd Edition)
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