Calculus and Its Applications, Books a la Carte Plus MyLab Math Access Card Package (11th Edition)
11th Edition
ISBN: 9780133862386
Author: Marvin L. Bittinger, David J. Ellenbogen, Scott J. Surgent
Publisher: PEARSON
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Chapter PSDT, Problem 10BP
Find the slope and y-intercept of
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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]
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 Marks
Chapter PSDT Solutions
Calculus and Its Applications, Books a la Carte Plus MyLab Math Access Card Package (11th Edition)
Ch. PSDT - Express each of the following without an...Ch. PSDT - Express each of the following without an...Ch. PSDT - Express each of the following without an...Ch. PSDT - Prob. 4APCh. PSDT - Express each of the following without an exponent....Ch. PSDT - Prob. 6APCh. PSDT - Prob. 7APCh. PSDT - Prob. 8APCh. PSDT - Prob. 9APCh. PSDT - Multiply. Express each answer without a negative...
Ch. PSDT - Multiply. Express each answer without a negative...Ch. PSDT - Divide. Express each answer without a negative...Ch. PSDT - Prob. 13APCh. PSDT - Simplify. Express each answer without a negative...Ch. PSDT - Simplify. Express each answer without a negative...Ch. PSDT - Multiply. 3(x5)Ch. PSDT - Multiply. (x5)(x+3)Ch. PSDT - Multiply.
18.
Ch. PSDT - Prob. 19APCh. PSDT - Multiply.
20.
Ch. PSDT - Prob. 21APCh. PSDT - Factor. x26xy+9y2Ch. PSDT - Factor.
23.
Ch. PSDT - Factor. 6x2+7x5Ch. PSDT - Factor.
25.
Ch. PSDT - Solve.
26.
Ch. PSDT - Solve.
27.
Ch. PSDT - Solve.
28.
Ch. PSDT - Solve.
29.
Ch. PSDT - Solve.
30.
Ch. PSDT - Solve.
31. After a 5% gain in weight, a grizzly...Ch. PSDT - Solve. Raggs, Ltd., a clothing firm, determines...Ch. PSDT - Graph. y=2x+1Ch. PSDT - Prob. 2BPCh. PSDT - Prob. 3BPCh. PSDT - Prob. 4BPCh. PSDT - A function f is given by f(x)=3x22x+8. Find each...Ch. PSDT - A function f is given by f(x)=(x+3)24. Find all x...Ch. PSDT - Prob. 7BPCh. PSDT - Write interval notation for {x| 4x5}.Ch. PSDT - 9. Find the domain
Ch. PSDT - 10. Find the slope and y-intercept of
Ch. PSDT - 11. Find an equation of the line that has slope 3...Ch. PSDT - 12. Find the slope of the line containing the...Ch. PSDT - Prob. 13BPCh. PSDT - Graph.
14.
Ch. PSDT - Graph. f(x)=1xCh. PSDT - Graph.
16.
Ch. PSDT - Graph. f(x)=xCh. PSDT - 18. Suppose that $1000 is invested at 5%,...
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