Precalculus Plus MyLab Math with eText -- Access Card Package (10th Edition) (Sullivan & Sullivan Precalculus Titles)
10th Edition
ISBN: 9780321978981
Author: Michael Sullivan
Publisher: PEARSON
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Chapter 12.5, Problem 43AYU
To determine
To find: The numerical value of correct to five decimal places.
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The final answer is 8/π(sinx) + 8/3π(sin 3x)+ 8/5π(sin5x)....
Keity
x२
1. (i)
Identify which of the following subsets of R2 are open and which
are not.
(a)
A = (2,4) x (1, 2),
(b)
B = (2,4) x {1,2},
(c)
C = (2,4) x R.
Provide a sketch and a brief explanation to each of your answers.
[6 Marks]
(ii)
Give an example of a bounded set in R2 which is not open.
[2 Marks]
(iii)
Give an example of an open set in R2 which is not bounded.
[2 Marks
2.
(i)
Which of the following statements are true? Construct coun-
terexamples for those that are false.
(a)
sequence.
Every bounded sequence (x(n)) nEN C RN has a convergent sub-
(b)
(c)
(d)
Every sequence (x(n)) nEN C RN has a convergent subsequence.
Every convergent sequence (x(n)) nEN C RN is bounded.
Every bounded sequence (x(n)) EN CRN converges.
nЄN
(e)
If a sequence (xn)nEN C RN has a convergent subsequence, then
(xn)nEN is convergent.
[10 Marks]
(ii)
Give an example of a sequence (x(n))nEN CR2 which is located on
the parabola x2 = x², contains infinitely many different points and converges
to the limit x = (2,4).
[5 Marks]
Chapter 12 Solutions
Precalculus Plus MyLab Math with eText -- Access Card Package (10th Edition) (Sullivan & Sullivan Precalculus Titles)
Ch. 12.1 - For the function f( x )= x1 x , find f( 2 ) and f(...Ch. 12.1 - True or False A function is a relation between two...Ch. 12.1 - Prob. 3AYUCh. 12.1 - True or False The notation a 5 represents the...Ch. 12.1 - True or False If is am integer, then
Ch. 12.1 - The sequence a 1 =5 , a n =3 a n1 is an example of...Ch. 12.1 - The notation a 1 + a 2 + a 3 ++ a n = k=1 n a k...Ch. 12.1 - Prob. 8AYUCh. 12.1 - In Problems 11-16, evaluate each factorial...Ch. 12.1 - Prob. 10AYU
Ch. 12.1 - Prob. 11AYUCh. 12.1 - In Problems 11-16, evaluate each factorial...Ch. 12.1 - Prob. 13AYUCh. 12.1 - In Problems 11-16, evaluate each factorial...Ch. 12.1 - In Problems 17-28, write down the first five terms...Ch. 12.1 - Prob. 16AYUCh. 12.1 - In Problems 17-28, write down the first five terms...Ch. 12.1 - In Problems 17-28, write down the first five terms...Ch. 12.1 - In Problems 17-28, write down the first five terms...Ch. 12.1 - In Problems 17-28, write down the first five terms...Ch. 12.1 - In Problems 17-28, write down the first five terms...Ch. 12.1 - In Problems 17-28, write down the first five terms...Ch. 12.1 - In Problems 17-28, write down the first five terms...Ch. 12.1 - In Problems 17-28, write down the first five terms...Ch. 12.1 - In Problems 17-28, write down the first five terms...Ch. 12.1 - In Problems 17-28, write down the first five terms...Ch. 12.1 - In Problems 29-36, the given pattern continues....Ch. 12.1 - Prob. 28AYUCh. 12.1 - In Problems 29-36, the given pattern continues....Ch. 12.1 - In Problems 29-36, the given pattern continues....Ch. 12.1 - In Problems 29-36, the given pattern continues....Ch. 12.1 - In Problems 29-36, the given pattern continues....Ch. 12.1 - In Problems 29-36, the given pattern continues....Ch. 12.1 - In Problems 29-36, the given pattern continues....Ch. 12.1 - In Problems 37-50, a sequence is defined...Ch. 12.1 - In Problems 37-50, a sequence is defined...Ch. 12.1 - In Problems 37-50, a sequence is defined...Ch. 12.1 - In Problems 37-50, a sequence is defined...Ch. 12.1 - Prob. 39AYUCh. 12.1 - In Problems 37-50, a sequence is defined...Ch. 12.1 - In Problems 37-50, a sequence is defined...Ch. 12.1 - Prob. 42AYUCh. 12.1 - In Problems 37-50, a sequence is defined...Ch. 12.1 - In Problems 37-50, a sequence is defined...Ch. 12.1 - In Problems 37-50, a sequence is defined...Ch. 12.1 - In Problems 37-50, a sequence is defined...Ch. 12.1 - In Problems 37-50, a sequence is defined...Ch. 12.1 - In Problems 37-50, a sequence is defined...Ch. 12.1 - In Problems 51-60, write out each sum. k=1 n (...Ch. 12.1 - In Problems 51-60, write out each sum. k=1 n (...Ch. 12.1 - In Problems 51-60, write out each sum. k=1 n k 2...Ch. 12.1 - In Problems 51-60, write out each sum. k=1 n (...Ch. 12.1 - In Problems 51-60, write out each sum. k=0 n 1 3...Ch. 12.1 - In Problems 51-60, write out each sum. k=0 n ( 3...Ch. 12.1 - In Problems 51-60, write out each sum. k=0 n1 1 3...Ch. 12.1 - In Problems 51-60, write out each sum. k=0 n1 (...Ch. 12.1 - In Problems 51-60, write out each sum. k=2 n ( 1...Ch. 12.1 - In Problems 51-60, write out each sum. k=3 n ( 1...Ch. 12.1 - In Problems 61-70, express each sum using...Ch. 12.1 - In Problems 61-70, express each sum using...Ch. 12.1 - In Problems 61-70, express each sum using...Ch. 12.1 - In Problems 61-70, express each sum using...Ch. 12.1 - In Problems 61-70, express each sum using...Ch. 12.1 - In Problems 61-70, express each sum using...Ch. 12.1 - In Problems 61-70, express each sum using...Ch. 12.1 - In Problems 61-70, express each sum using...Ch. 12.1 - In Problems 61-70, express each sum using...Ch. 12.1 - In Problems 61-70, express each sum using...Ch. 12.1 - In Problems 71-82, find the sum of each sequence. ...Ch. 12.1 - In Problems 71-82, find the sum of each sequence. ...Ch. 12.1 - In Problems 71-82, find the sum of each sequence. ...Ch. 12.1 - In Problems 71-82, find the sum of each sequence. ...Ch. 12.1 - In Problems 71-82, find the sum of each sequence. ...Ch. 12.1 - In Problems 71-82, find the sum of each sequence. ...Ch. 12.1 - In Problems 71-82, find the sum of each sequence. ...Ch. 12.1 - In Problems 71-82, find the sum of each sequence. ...Ch. 12.1 - In Problems 71-82, find the sum of each sequence. ...Ch. 12.1 - In Problems 71-82, find the sum of each sequence. ...Ch. 12.1 - In Problems 71-82, find the sum of each sequence. ...Ch. 12.1 - Credit Card Debt John has a balance of on his...Ch. 12.1 - Trout Population A pond currently contains 2000...Ch. 12.1 - Car Loans Phil bought a car by taking out a loan...Ch. 12.1 - Environmental Control The Environmental Protection...Ch. 12.1 - Growth of a Rabbit Colony A colony of rabbits...Ch. 12.1 - The Pascal Triangle The triangular array shown,...Ch. 12.1 - Prob. 88AYUCh. 12.1 - Prob. 97AYUCh. 12.1 - Prob. 98AYUCh. 12.1 - Prob. 99AYUCh. 12.1 - Prob. 101AYUCh. 12.1 - Prob. 102AYUCh. 12.1 - Prob. 103AYUCh. 12.1 - Prob. 104AYUCh. 12.1 - Prob. 105AYUCh. 12.2 - In a(n) _________ sequence, the difference between...Ch. 12.2 - Prob. 2AYUCh. 12.2 - If the 5th term of an arithmetic sequence is 12...Ch. 12.2 - True or False The sum S n of the first n terms of...Ch. 12.2 - Prob. 5AYUCh. 12.2 - If a n =2n+7 is the n th term of an arithmetic...Ch. 12.2 - In Problems 7-16, show that each sequence is...Ch. 12.2 - In Problems 7-16, show that each sequence is...Ch. 12.2 - In Problems 7-16, show that each sequence is...Ch. 12.2 - In Problems 7-16, show that each sequence is...Ch. 12.2 - In Problems 7-16, show that each sequence is...Ch. 12.2 - In Problems 7-16, show that each sequence is...Ch. 12.2 - In Problems 7-16, show that each sequence is...Ch. 12.2 - In Problems 7-16, show that each sequence is...Ch. 12.2 - In Problems 7-16, show that each sequence is...Ch. 12.2 - In Problems 7-16, show that each sequence is...Ch. 12.2 - In Problems 17-24, find the nth term of the...Ch. 12.2 - In Problems 17-24, find the nth term of the...Ch. 12.2 - Prob. 19AYUCh. 12.2 - In Problems 17-24, find the nth term of the...Ch. 12.2 - In Problems 17-24, find the nth term of the...Ch. 12.2 - In Problems 17-24, find the nth term of the...Ch. 12.2 - In Problems 17-24, find the nth term of the...Ch. 12.2 - In Problems 17-24, find the nth term of the...Ch. 12.2 - In Problems 25-30, find the indicated term in each...Ch. 12.2 - In Problems 25-30, find the indicated term in each...Ch. 12.2 - Prob. 27AYUCh. 12.2 - In Problems 25-30, find the indicated term in each...Ch. 12.2 - In Problems 25-30, find the indicated term in each...Ch. 12.2 - In Problems 25-30, find the indicated term in each...Ch. 12.2 - In Problems 31-38, find the first term and the...Ch. 12.2 - In Problems 31-38, find the first term and the...Ch. 12.2 - In Problems 31-38, find the first term and the...Ch. 12.2 - In Problems 31-38, find the first term and the...Ch. 12.2 - In Problems 31-38, find the first term and the...Ch. 12.2 - In Problems 31-38, find the first term and the...Ch. 12.2 - In Problems 31-38, find the first term and the...Ch. 12.2 - In Problems 31-38, find the first term and the...Ch. 12.2 - In Problems 39-56, find each sum. 1+3+5++( 2n1 )Ch. 12.2 - In Problems 39-56, find each sum. 2+4+6++2nCh. 12.2 - In Problems 39-56, find each sum. 7+12+17++( 2+5n...Ch. 12.2 - In Problems 39-56, find each sum. 1+3+7++( 4n5 )Ch. 12.2 - In Problems 39-56, find each sum. 2+4+6++70Ch. 12.2 - In Problems 39-56, find each sum. 1+3+5++59Ch. 12.2 - Prob. 45AYUCh. 12.2 - Prob. 46AYUCh. 12.2 - Prob. 47AYUCh. 12.2 - In Problems 39-56, find each sum. 7+1511299Ch. 12.2 - In Problems 39-56, find each sum. 4+4.5+5+5.5++100Ch. 12.2 - In Problems 39-56, find each sum. 8+8 1 4 +8 1 2...Ch. 12.2 - Prob. 51AYUCh. 12.2 - Prob. 52AYUCh. 12.2 - In Problems 39-56, find each sum. n=1 100 ( 6 1 2...Ch. 12.2 - Prob. 54AYUCh. 12.2 - Prob. 55AYUCh. 12.2 - In Problems 39-56, find each sum. The sum of the...Ch. 12.2 - Prob. 57AYUCh. 12.2 - Prob. 58AYUCh. 12.2 - How many terms must be added in an arithmetic...Ch. 12.2 - How many terms must be added in an arithmetic...Ch. 12.2 - Drury Lane Theater The Drury Lane Theater has 25...Ch. 12.2 - Seats in an Amphitheater An outdoor amphitheater...Ch. 12.2 - Prob. 62AYUCh. 12.2 - Prob. 64AYUCh. 12.2 - Salary If you take a job with a starting salary of...Ch. 12.2 - Stadium Construction How many rows are in the...Ch. 12.2 - Creating a Mosaic A mosaic is designed in the...Ch. 12.2 - Cooling Air As a parcel of air rises (for example,...Ch. 12.2 - Prob. 66AYUCh. 12.2 - Prob. 70AYUCh. 12.2 - Prob. 71AYUCh. 12.2 - Prob. 72AYUCh. 12.2 - Prob. 73AYUCh. 12.2 - Prob. 74AYUCh. 12.2 - Prob. 75AYUCh. 12.3 - If is invested at per annum compounded...Ch. 12.3 - Prob. 2AYUCh. 12.3 - In a(n) _____________ sequence, the ratio of...Ch. 12.3 - Prob. 4AYUCh. 12.3 - Prob. 5AYUCh. 12.3 - Prob. 6AYUCh. 12.3 - Prob. 7AYUCh. 12.3 - Prob. 8AYUCh. 12.3 - In problems 918, show that each sequence is...Ch. 12.3 - In Problems 9-18, show that each sequence is...Ch. 12.3 - Prob. 11AYUCh. 12.3 - In Problems 9-18, show that each sequence is...Ch. 12.3 - In Problems 9-18, show that each sequence is...Ch. 12.3 - In Problems 9-18, show that each sequence is...Ch. 12.3 - Prob. 15AYUCh. 12.3 - In Problems 9-18, show that each sequence is...Ch. 12.3 - In Problems 9-18, show that each sequence is...Ch. 12.3 - In Problems 9-18, show that each sequence is...Ch. 12.3 - In Problems 19-26, find the fifth term and the n...Ch. 12.3 - In Problems 19-26, find the fifth term and the n...Ch. 12.3 - In Problems 19-26, find the fifth term and the n...Ch. 12.3 - In Problems 19-26, find the fifth term and the n...Ch. 12.3 - In Problems 19-26, find the fifth term and the n...Ch. 12.3 - In Problems 19-26, find the fifth term and the n...Ch. 12.3 - Prob. 25AYUCh. 12.3 - In Problems 19-26, find the fifth term and the n...Ch. 12.3 - In Problems 27-32, find the indicated term of each...Ch. 12.3 - In Problems 27-32, find the indicated term of each...Ch. 12.3 - Prob. 29AYUCh. 12.3 - In Problems 27-32, find the indicated term of each...Ch. 12.3 - In Problems 27-32, find the indicated term of each...Ch. 12.3 - In Problems 27-32, find the indicated term of each...Ch. 12.3 - Prob. 33AYUCh. 12.3 - In Problems 33-40, find the n th term a n of each...Ch. 12.3 - In Problems 33-40, find the n th term a n of each...Ch. 12.3 - In Problems 33-40, find the n th term a n of each...Ch. 12.3 - In Problems 33-40, find the n th term a n of each...Ch. 12.3 - In Problems 33-40, find the n th term a n of each...Ch. 12.3 - In Problems 33-40, find the n th term a n of each...Ch. 12.3 - In Problems 33-40, find the n th term a n of each...Ch. 12.3 - In problems 41-46, find each sum. 1 4 + 2 4 + 2 2...Ch. 12.3 - In problems 41-46, find each sum. 3 9 + 3 2 9 + 3...Ch. 12.3 - In problems 41-46, find each sum. k=1 n ( 2 3 ) kCh. 12.3 - In problems 41-46, find each sum. k=1 n 4 3 k1Ch. 12.3 - In problems 41-46, find each sum. 1248( 2 n1 )Ch. 12.3 - In problems 41-46, find each sum. 2+ 6 5 + 18 25...Ch. 12.3 - Prob. 47AYUCh. 12.3 - Prob. 48AYUCh. 12.3 - Prob. 49AYUCh. 12.3 - Prob. 50AYUCh. 12.3 - Prob. 51AYUCh. 12.3 - Prob. 52AYUCh. 12.3 - In Problems 53-68, determine whether each infinite...Ch. 12.3 - In Problems 53-68, determine whether each infinite...Ch. 12.3 - In Problems 53-68, determine whether each infinite...Ch. 12.3 - In Problems 53-68, determine whether each infinite...Ch. 12.3 - In Problems 53-68, determine whether each infinite...Ch. 12.3 - In Problems 53-68, determine whether each infinite...Ch. 12.3 - In Problems 53-68, determine whether each infinite...Ch. 12.3 - In Problems 53-68, determine whether each infinite...Ch. 12.3 - In Problems 53-68, determine whether each infinite...Ch. 12.3 - In Problems 53-68, determine whether each infinite...Ch. 12.3 - In Problems 53-68, determine whether each infinite...Ch. 12.3 - In Problems 53-68, determine whether each infinite...Ch. 12.3 - In Problems 53-68, determine whether each infinite...Ch. 12.3 - In Problems 53-68, determine whether each infinite...Ch. 12.3 - In Problems 53-68, determine whether each infinite...Ch. 12.3 - Prob. 68AYUCh. 12.3 - Prob. 69AYUCh. 12.3 - Prob. 70AYUCh. 12.3 - Prob. 71AYUCh. 12.3 - Prob. 72AYUCh. 12.3 - Prob. 73AYUCh. 12.3 - Prob. 74AYUCh. 12.3 - Prob. 75AYUCh. 12.3 - Prob. 76AYUCh. 12.3 - Prob. 77AYUCh. 12.3 - Prob. 78AYUCh. 12.3 - Prob. 79AYUCh. 12.3 - Prob. 80AYUCh. 12.3 - Prob. 81AYUCh. 12.3 - Prob. 82AYUCh. 12.3 - Prob. 83AYUCh. 12.3 - Prob. 84AYUCh. 12.3 - Prob. 85AYUCh. 12.3 - Prob. 86AYUCh. 12.3 - Prob. 87AYUCh. 12.3 - Prob. 88AYUCh. 12.3 - Retirement Christine contributes each month to...Ch. 12.3 - Saving for a home Jolene wants to purchase a new...Ch. 12.3 - Prob. 91AYUCh. 12.3 - Retirement Ray contributes 1000 to an individual...Ch. 12.3 - Prob. 93AYUCh. 12.3 - Prob. 94AYUCh. 12.3 - Prob. 95AYUCh. 12.3 - Prob. 96AYUCh. 12.3 - Multiplier Suppose that, throughout the U.S....Ch. 12.3 - Multiplier Refer to Problem 97. Suppose that the...Ch. 12.3 - Prob. 99AYUCh. 12.3 - Prob. 100AYUCh. 12.3 - Prob. 101AYUCh. 12.3 - Seating Revenue A special section in the end zone...Ch. 12.3 - Prob. 103AYUCh. 12.3 - Prob. 104AYUCh. 12.3 - Prob. 105AYUCh. 12.3 - Prob. 106AYUCh. 12.3 - Prob. 107AYUCh. 12.3 - Prob. 108AYUCh. 12.3 - Prob. 109AYUCh. 12.3 - Prob. 110AYUCh. 12.3 - Prob. 111AYUCh. 12.3 - Prob. 112AYUCh. 12.3 - Prob. 113AYUCh. 12.3 - Prob. 114AYUCh. 12.4 - In Problems 1-22, use the Principle of...Ch. 12.4 - In Problems 1-22, use the Principle of...Ch. 12.4 - In Problems 1-22, use the Principle of...Ch. 12.4 - In Problems 1-22, use the Principle of...Ch. 12.4 - In Problems 1-22, use the Principle of...Ch. 12.4 - In Problems 1-22, use the Principle of...Ch. 12.4 - In Problems 1-22, use the Principle of...Ch. 12.4 - In Problems 1-22, use the Principle of...Ch. 12.4 - In Problems 1-22, use the Principle of...Ch. 12.4 - In Problems 1-22, use the Principle of...Ch. 12.4 - In Problems 1-22, use the Principle of...Ch. 12.4 - In Problems 1-22, use the Principle of...Ch. 12.4 - In Problems 1-22, use the Principle of...Ch. 12.4 - In Problems 1-22, use the Principle of...Ch. 12.4 - In Problems 1-22, use the Principle of...Ch. 12.4 - In Problems 1-22, use the Principle of...Ch. 12.4 - In Problems 1-22, use the Principle of...Ch. 12.4 - In Problems 1-22, use the Principle of...Ch. 12.4 - In Problems 1-22, use the Principle of...Ch. 12.4 - In Problems 1-22, use the Principle of...Ch. 12.4 - Prob. 21AYUCh. 12.4 - Prob. 22AYUCh. 12.4 - Prob. 23AYUCh. 12.4 - Prob. 24AYUCh. 12.4 - Prob. 25AYUCh. 12.4 - Prob. 26AYUCh. 12.4 - Prob. 27AYUCh. 12.4 - Prob. 28AYUCh. 12.4 - Prob. 29AYUCh. 12.4 - Prob. 30AYUCh. 12.4 - Prob. 31AYUCh. 12.4 - Extended Principle of Mathematical Induction The...Ch. 12.4 - Geometry Use the Extended Principle of...Ch. 12.4 - How would you explain the Principle of...Ch. 12.4 - Prob. 35AYUCh. 12.4 - Prob. 37AYUCh. 12.4 - A mass of 500 kg is suspended from two cables, as...Ch. 12.4 - Prob. 38AYUCh. 12.5 - The ______ ______ is a triangular display of the...Ch. 12.5 - Prob. 2AYUCh. 12.5 - Prob. 3AYUCh. 12.5 - Prob. 4AYUCh. 12.5 - In Problems 5-16, evaluate each expression. ( 5 3...Ch. 12.5 - Prob. 6AYUCh. 12.5 - Prob. 7AYUCh. 12.5 - Prob. 8AYUCh. 12.5 - Prob. 9AYUCh. 12.5 - Prob. 10AYUCh. 12.5 - Prob. 11AYUCh. 12.5 - Prob. 12AYUCh. 12.5 - Prob. 13AYUCh. 12.5 - In Problems 5-16, evaluate each expression. ( 60...Ch. 12.5 - Prob. 15AYUCh. 12.5 - Prob. 16AYUCh. 12.5 - In Problems 17-28, expand each expression using...Ch. 12.5 - In Problems 17-28, expand each expression using...Ch. 12.5 - In Problems 17-28, expand each expression using...Ch. 12.5 - In Problems 17-28, expand each expression using...Ch. 12.5 - In Problems 17-28, expand each expression using...Ch. 12.5 - In Problems 17-28, expand each expression using...Ch. 12.5 - In Problems 17-28, expand each expression using...Ch. 12.5 - In Problems 17-28, expand each expression using...Ch. 12.5 - In Problems 17-28, expand each expression using...Ch. 12.5 - In Problems 17-28, expand each expression using...Ch. 12.5 - In Problems 17-28, expand each expression using...Ch. 12.5 - In Problems 17-28, expand each expression using...Ch. 12.5 - In Problems 29-42, use the Binomial Theorem to...Ch. 12.5 - In Problems 29-42, use the Binomial Theorem to...Ch. 12.5 - In Problems 29-42, use the Binomial Theorem to...Ch. 12.5 - In Problems 29-42, use the Binomial Theorem to...Ch. 12.5 - In Problems 29-42, use the Binomial Theorem to...Ch. 12.5 - In Problems 29-42, use the Binomial Theorem to...Ch. 12.5 - In Problems 29-42, use the Binomial Theorem to...Ch. 12.5 - In Problems 29-42, use the Binomial Theorem to...Ch. 12.5 - In Problems 29-42, use the Binomial Theorem to...Ch. 12.5 - In Problems 29-42, use the Binomial Theorem to...Ch. 12.5 - In Problems 29-42, use the Binomial Theorem to...Ch. 12.5 - Prob. 40AYUCh. 12.5 - Prob. 41AYUCh. 12.5 - Prob. 42AYUCh. 12.5 - Prob. 43AYUCh. 12.5 - Prob. 44AYUCh. 12.5 - Show that ( n n1 )=nand( n n )=1 .Ch. 12.5 - Show that if n and j are integers with 0jn, then,...Ch. 12.5 - Prob. 47AYUCh. 12.5 - Prob. 48AYUCh. 12.5 - Prob. 49AYUCh. 12.5 - Prob. 50AYUCh. 12.5 - Prob. 51AYUCh. 12.5 - Prob. 52AYUCh. 12.5 - Prob. 53AYUCh. 12.5 - Prob. 54AYUCh. 12 - In Problems , list the five terms of each...Ch. 12 - In Problems 14, list the five terms of each...Ch. 12 - Prob. 3RECh. 12 - In Problems 14, list the five terms of each...Ch. 12 - Expand .
Ch. 12 - Prob. 6RECh. 12 - In Problems 712, determine whether the given...Ch. 12 - In Problems , determine whether the given sequence...Ch. 12 - In Problems , determine whether the given sequence...Ch. 12 - In Problems , determine whether the given sequence...Ch. 12 - In Problems 712, determine whether the given...Ch. 12 - In Problems , determine whether the given sequence...Ch. 12 - In Problems , find each sum.
Ch. 12 - In Problems 1316, find each sum. k=140(2k+8)Ch. 12 - In Problems , find each sum.
Ch. 12 - In Problems 1316, find each sum. k=110(2k)Ch. 12 - In Problems 1719, find the indicated term in each...Ch. 12 - In Problems 1719, find the indicated term in each...Ch. 12 - In Problems , find the indicated term in each...Ch. 12 - In Problems 20and 21, find a general formula for...Ch. 12 - In Problems 20and 21, find a general formula for...Ch. 12 - In Problems 2225, determine whether each infinite...Ch. 12 - In Problems 2225, determine whether each infinite...Ch. 12 - In Problems , determine whether each infinite...Ch. 12 - In Problems , determine whether each infinite...Ch. 12 - In Problems , use the Principle of Mathematical...Ch. 12 - Prob. 27RECh. 12 - In Problems , use the Principle of Mathematical...Ch. 12 - Prob. 29RECh. 12 - Prob. 30RECh. 12 - Prob. 31RECh. 12 - Prob. 32RECh. 12 - Prob. 33RECh. 12 - Constructing a Brick Staircase A brick staircase...Ch. 12 - Creating a Floor Design A mosaic tile floor is...Ch. 12 - Bouncing Balls A ball is dropped from a height of...Ch. 12 - Prob. 37RECh. 12 - Salary Increases Your friend has just been hired...Ch. 12 - Prob. 1CTCh. 12 - Prob. 2CTCh. 12 - Prob. 3CTCh. 12 - Prob. 4CTCh. 12 - Prob. 5CTCh. 12 - Prob. 6CTCh. 12 - Prob. 7CTCh. 12 - Prob. 8CTCh. 12 - Prob. 9CTCh. 12 - Prob. 10CTCh. 12 - Prob. 11CTCh. 12 - Prob. 12CTCh. 12 - Prob. 13CTCh. 12 - Prob. 14CTCh. 12 - Prob. 15CTCh. 12 - A weightlifter begins his routine by benching ...Ch. 12 - Prob. 1CRCh. 12 - Prob. 2CRCh. 12 - Prob. 3CRCh. 12 - Prob. 4CRCh. 12 - Prob. 5CRCh. 12 - Prob. 6CRCh. 12 - Prob. 7CRCh. 12 - Prob. 8CRCh. 12 - Prob. 9CRCh. 12 - Prob. 10CRCh. 12 - Prob. 11CRCh. 12 - Prob. 12CR
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- 2. (i) What does it mean to say that a sequence (x(n)) nEN CR2 converges to the limit x E R²? [1 Mark] (ii) Prove that if a set ECR2 is closed then every convergent sequence (x(n))nen in E has its limit in E, that is (x(n)) CE and x() x x = E. [5 Marks] (iii) which is located on the parabola x2 = = x x4, contains a subsequence that Give an example of an unbounded sequence (r(n)) nEN CR2 (2, 16) and such that x(i) converges to the limit x = (2, 16) and such that x(i) # x() for any i j. [4 Marksarrow_forward1. (i) which are not. Identify which of the following subsets of R2 are open and (a) A = (1, 3) x (1,2) (b) B = (1,3) x {1,2} (c) C = AUB (ii) Provide a sketch and a brief explanation to each of your answers. [6 Marks] Give an example of a bounded set in R2 which is not open. (iii) [2 Marks] Give an example of an open set in R2 which is not bounded. [2 Marks]arrow_forward2. if limit. Recall that a sequence (x(n)) CR2 converges to the limit x = R² lim ||x(n)x|| = 0. 818 - (i) Prove that a convergent sequence (x(n)) has at most one [4 Marks] (ii) Give an example of a bounded sequence (x(n)) CR2 that has no limit and has accumulation points (1, 0) and (0, 1) [3 Marks] (iii) Give an example of a sequence (x(n))neN CR2 which is located on the hyperbola x2 1/x1, contains infinitely many different Total marks 10 points and converges to the limit x = (2, 1/2). [3 Marks]arrow_forward
- 3. (i) Consider a mapping F: RN Rm. Explain in your own words the relationship between the existence of all partial derivatives of F and dif- ferentiability of F at a point x = RN. (ii) [3 Marks] Calculate the gradient of the following function f: R2 → R, f(x) = ||x||3, Total marks 10 where ||x|| = √√√x² + x/2. [7 Marks]arrow_forward1. (i) (ii) which are not. What does it mean to say that a set ECR2 is closed? [1 Mark] Identify which of the following subsets of R2 are closed and (a) A = [-1, 1] × (1, 3) (b) B = [-1, 1] x {1,3} (c) C = {(1/n², 1/n2) ER2 | n EN} Provide a sketch and a brief explanation to each of your answers. [6 Marks] (iii) Give an example of a closed set which does not have interior points. [3 Marks]arrow_forwardA company specializing in lubrication products for vintage motors produce two blended oils, Smaza and Nefkov. They make a profit of K5,000.00 per litre of Smaza and K4,000.00 per litre of Nefkov. A litre of Smaza requires 0.4 litres of heavy oil and 0.6 litres of light oil. A litre of Nefkov requires 0.8 litres of heavy oil and 0.2 litres of light oil. The company has 100 litres of heavy oil and 80 litres of light oil. How many litres of each product should they make to maximize profits and what level of profit will they obtain? Show all your workings.arrow_forward
- 1. Show that the vector field F(x, y, z) = (2x sin ye³)ix² cos yj + (3xe³ +5)k satisfies the necessary conditions for a conservative vector field, and find a potential function for F.arrow_forward1. Newton's Law of Gravitation (an example of an inverse square law) states that the magnitude of the gravitational force between two objects with masses m and M is |F| mMG |r|2 where r is the distance between the objects, and G is the gravitational constant. Assume that the object with mass M is located at the origin in R³. Then, the gravitational force field acting on the object at the point r = (x, y, z) is given by F(x, y, z) = mMG r3 r. mMG mMG Show that the scalar vector field f(x, y, z) = = is a potential function for r √√x² + y² . Fi.e. show that F = Vf. Remark: f is the negative of the physical potential energy, because F = -V(-ƒ).arrow_forward2. Suppose f(x) = 3x² - 5x. Show all your work for the problems below.arrow_forward
- write it down for better understanding pleasearrow_forward1. Suppose F(t) gives the temperature in degrees Fahrenheit t minutes after 1pm. With a complete sentence, interpret the equation F(10) 68. (Remember this means explaining the meaning of the equation without using any mathy vocabulary!) Include units. (3 points) =arrow_forward2. Suppose f(x) = 3x² - 5x. Show all your work for the problems below. a. Evaluate f(-3). If you have multiple steps, be sure to connect your expressions with EQUALS SIGNS. (3 points)arrow_forward
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