CALCULUS & ITS APPLICATIONS MYLAB
12th Edition
ISBN: 9780136423287
Author: BITTINGER
Publisher: PEARSON
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Chapter B, Problem 3E
To determine
To find:
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(1) Write the following quadratic equation in terms of the vertex coordinates.
The final answer is 8/π(sinx) + 8/3π(sin 3x)+ 8/5π(sin5x)....
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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
Chapter B Solutions
CALCULUS & ITS APPLICATIONS MYLAB
Ch. B - Prob. 1ECh. B - Evaluate each limit. Use lHĂ´pitals Rule when...Ch. B - Prob. 3ECh. B - Prob. 4ECh. B - Prob. 5ECh. B - Prob. 6ECh. B - Prob. 7ECh. B - Prob. 8ECh. B - Evaluate each limit. Use lHĂ´pitals Rule when...Ch. B - Evaluate each limit. Use lHĂ´pitals Rule when...
Ch. B - Evaluate each limit. Use lHĂ´pitals Rule when...Ch. B - Prob. 12ECh. B - Prob. 13ECh. B - Prob. 14ECh. B - Prob. 15ECh. B - Prob. 16ECh. B - Evaluate each limit. Use lHĂ´pitals Rule when...Ch. B - Evaluate each limit. Use lHĂ´pitals Rule when...Ch. B - Evaluate each limit. Use lHĂ´pitals Rule when...Ch. B - Prob. 20ECh. B - Prob. 21ECh. B - Prob. 22ECh. B - Prob. 23ECh. B - Prob. 24ECh. B - Evaluate each limit. Use lHĂ´pitals Rule when...Ch. B - Evaluate each limit. Use lHĂ´pitals Rule when...Ch. B - Prob. 27ECh. B - Prob. 28ECh. B - Prob. 29ECh. B - Prob. 30ECh. B - Prob. 31ECh. B - Evaluate limx1x26xxCh. B - Evaluate limxx24xxx2+10xxCh. B - Prob. 34ECh. B - Prob. 35ECh. B - Prob. 38E
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- 2. 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_forward3. (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_forward
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