Calculus for Business, Economics, Life Sciences, and Social Sciences - Boston U.
15th Edition
ISBN: 9781323047620
Author: Barnett, Ziegler, Byleen
Publisher: Pearson Education
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Textbook Question
Chapter A.1, Problem 44E
In Problems 41–44, without using a calculator, round to the nearest integer.
44. (A)
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By considering appropriate series expansions,
e². e²²/2. e²³/3.
....
=
= 1 + x + x² + ·
...
when |x| < 1.
By expanding each individual exponential term on the left-hand side
the coefficient of x- 19 has the form
and multiplying out,
1/19!1/19+r/s,
where 19 does not divide s. Deduce that
18! 1 (mod 19).
Proof: LN⎯⎯⎯⎯⎯LN¯ divides quadrilateral KLMN into two triangles. The sum of the angle measures in each triangle is ˚, so the sum of the angle measures for both triangles is ˚. So, m∠K+m∠L+m∠M+m∠N=m∠K+m∠L+m∠M+m∠N=˚. Because ∠K≅∠M∠K≅∠M and ∠N≅∠L, m∠K=m∠M∠N≅∠L, m∠K=m∠M and m∠N=m∠Lm∠N=m∠L by the definition of congruence. By the Substitution Property of Equality, m∠K+m∠L+m∠K+m∠L=m∠K+m∠L+m∠K+m∠L=°,°, so (m∠K)+ m∠K+ (m∠L)= m∠L= ˚. Dividing each side by gives m∠K+m∠L=m∠K+m∠L= °.°. The consecutive angles are supplementary, so KN⎯⎯⎯⎯⎯⎯∥LM⎯⎯⎯⎯⎯⎯KN¯∥LM¯ by the Converse of the Consecutive Interior Angles Theorem. Likewise, (m∠K)+m∠K+ (m∠N)=m∠N= ˚, or m∠K+m∠N=m∠K+m∠N= ˚. So these consecutive angles are supplementary and KL⎯⎯⎯⎯⎯∥NM⎯⎯⎯⎯⎯⎯KL¯∥NM¯ by the Converse of the Consecutive Interior Angles Theorem. Opposite sides are parallel, so quadrilateral KLMN is a parallelogram.
By considering appropriate series expansions,
ex · ex²/2 . ¸²³/³ . . ..
=
= 1 + x + x² +……
when |x| < 1.
By expanding each individual exponential term on the left-hand side
and multiplying out, show that the coefficient of x 19 has the form
1/19!+1/19+r/s,
where 19 does not divide s.
Chapter A.1 Solutions
Calculus for Business, Economics, Life Sciences, and Social Sciences - Boston U.
Ch. A.1 - State the real number property that justifies the...Ch. A.1 - Prob. 2MPCh. A.1 - You intend to give a 20% tip, rounded to the...Ch. A.1 - In Problems 16, replace each question mark with an...Ch. A.1 - Prob. 2ECh. A.1 - Prob. 3ECh. A.1 - In Problems 16, replace each question mark with an...Ch. A.1 - In Problems 16, replace each question mark with an...Ch. A.1 - In Problems 16, replace each question mark with an...Ch. A.1 - In Problems 726, indicate true (T) or false (F)....
Ch. A.1 - In Problems 726, indicate true (T) or false (F)....Ch. A.1 - In Problems 726, indicate true (T) or false (F)....Ch. A.1 - In Problems 726, indicate true (T) or false (F)....Ch. A.1 - In Problems 726, indicate true (T) or false (F)....Ch. A.1 - In Problems 726, indicate true (T) or false (F)....Ch. A.1 - In Problems 726, indicate true (T) or false (F)....Ch. A.1 - Prob. 14ECh. A.1 - In Problems 726, indicate true (T) or false (F)....Ch. A.1 - In Problems 726, indicate true (T) or false (F)....Ch. A.1 - In Problems 726, indicate true (T) or false (F)....Ch. A.1 - In Problems 726, indicate true (T) or false (F)....Ch. A.1 - In Problems 726, indicate true (T) or false (F)....Ch. A.1 - In Problems 726, indicate true (T) or false (F)....Ch. A.1 - Prob. 21ECh. A.1 - In Problems 726, indicate true (T) or false (F)....Ch. A.1 - In Problems 726, indicate true (T) or false (F)....Ch. A.1 - In Problems 726, indicate true (T) or false (F)....Ch. A.1 - In Problems 726, indicate true (T) or false (F)....Ch. A.1 - Prob. 26ECh. A.1 - Prob. 27ECh. A.1 - If uv = 0, does either u or v have to be 0 ?...Ch. A.1 - Indicate whether the following are true (T) or...Ch. A.1 - Indicate whether the following are true (T) or...Ch. A.1 - Prob. 31ECh. A.1 - Give an example of a rational number that is not...Ch. A.1 - Given the sets of numbers N (natural numbers), Z...Ch. A.1 - Prob. 34ECh. A.1 - Indicate true (T) or false (F), and for each false...Ch. A.1 - Indicate true (T) or false (F), and for each false...Ch. A.1 - Prob. 37ECh. A.1 - Repeat Problem 37 for 0.181818 . 37.If c =...Ch. A.1 - Use a calculator to express each number in...Ch. A.1 - Prob. 40ECh. A.1 - In Problems 4144, without using a calculator,...Ch. A.1 - Prob. 42ECh. A.1 - Prob. 43ECh. A.1 - In Problems 4144, without using a calculator,...Ch. A.1 - Sales tax. Find the tax owed on a purchase of...Ch. A.1 - Sales tax. If you paid 29.86 in tax on a purchase...Ch. A.1 - Gasoline prices. If the price per gallon of gas...Ch. A.1 - Prob. 48E
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