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clear explanation . tks (thumb) In this question you must state if you sandwich theorem. You do not need to justify usi...
Question 2 (10 marks) In this question you must state if you use any standard limits, continuity, l'Hôpital's r...
Question 2 (10 marks) In this question you must state if you use any standard limits, continuity, l'Hôpital's rule, the sandwich theorem or any convergence tests for series. You do not need to justify using limit laws 2n n3 or explain why it does not exist. (a) Evaluate lim n (b) Determine whether each of the following converge: n+3 2n (i) 2 (3n) (ii) (n3)! n=1
Question 2 (10 marks) In this question you must state if you use any...
1. Consider the function -F5 sin(r) for r f(x) =2 for 1< 3 2-25 for 3...
1. Consider the function -F5 sin(r) for r f(x) =2 for 1< 3 2-25 for 3 x2 -9x + 20 Evaluate the following limits You do not have to cite limit laws, but you must show how you arrived at your answer If a limit Does Not Exist, explain why. You should use oo or -oo where applicable Calculating the limit using L'Hopital's Rule will receive NO CREDIT. (a) lim f(x) r-+0 (b) lim f(x)= z-1 (e) lim f(z) (d)...
real analysis 1,3,8,11,12 please 4.4.3 4.4.11a Limits and Continuity 4 Chapter Remark: In the statement of T...
real analysis
1,3,8,11,12 please
4.4.3
4.4.11a
Limits and Continuity 4 Chapter Remark: In the statement of Theorem 4.4.12 we assumed that f was tone and continuous on the interval I. The fact that f is either stric tric. strictly decreasing on / implies that f is one-to-one on t one-to-one and continuous on an interval 1, then as a consequence of the value theorem the function f is strictly monotone on I (Exercise 15). This false if either f is...
Format requirement: Question 3. E-6 Proof (Show Working) 10 points 249 Show that f:RR defined by f(x) is continuous at x = 7 using only r +3 cosa the epsilon-delta definition of continuity. Note that...
Format requirement:
Question 3. E-6 Proof (Show Working) 10 points 249 Show that f:RR defined by f(x) is continuous at x = 7 using only r +3 cosa the epsilon-delta definition of continuity. Note that we want you to do it the hard way: you are not allowed to use the limit laws or the combination of continuous functions theorem or similar. You must give an 'e-δ style proof Solution: Let ε > 0 be given and choose δ =...
Do problems 1 and 3 please. Use any entries for the first problem. Thank you. 1....
Do problems 1 and 3 please. Use any entries for the first
problem. Thank you.
1. (a) Make a table, rounding all entries to four decimal digits, to estimate the instantaneous rate of change of f(x) = x° at x = 1. Round your final answer to three decimal digits (b) Briefly describe how the entries in your table relate to the graph f(x)= x. In addition, briefly explain how your final estimate relates to the graph of f(x) =...
Problem 3. Prove Theorem 1 as tollows [Assume all conditions of the Theorem are met. In many part...
Problem 3. Prove Theorem 1 as tollows [Assume all conditions of the Theorem are met. In many parts, it will be useful to consider the sign of the right side of the formula-positive or negative- ad to write the appropriate inequality] (a) Since f"(x) exists on [a, brx) is continuous on [a, b) and differentiable on (a,b), soMean Value Thorem applies to f,on this interval. Apply MVTtof"m[x,y], wherc α zcysb. to show that ry)2 f,(x), İ.e. that f, is increasing...
Write ‘T' for true or ‘F' for false. You do not need to show any work...
Write ‘T' for true or ‘F' for false. You do not need to show any work or justify your answers for this question. The questions are 2 points each. (a) __If (xn) is a convergent sequence (converging to a finite limit) and f:RR is a continuous function, then (f (xn)) is a convergent sequence. (b) _If (xn) is a Cauchy sequence with Yn € (0,1) and f :(0,1) + R is contin- uous, then (f(xn)) is also a Cauchy sequence....
f(T) = 22 9 Instructions: • If you are asked for a function, enter a function....
f(T) = 22 9 Instructions: • If you are asked for a function, enter a function. • If you are asked to find 2- or y-values, enter either a number or a list of numbers separated by commas. If there are no solutions, enter None. • If you are asked to find an interval or union of intervals, use interval notation. Enter { } if an interval is empty • If you are asked to find a limit, enter either...
Determine if the statement is True or False. You do not need to explain your choice....
Determine if the statement is True or False. You do not need to explain your choice. (T/F) a. Any two vectors can be added together. b. If I = c is not in the domain of f(x) and a <csb, then | slo) do f(1) dar is an improper integral (T/F) c. It is possible for a series (-1)*ax to converge and at to diverge. (T/F) d. The vectors u xv and v x u can never be equal. (T/F)...
This question is intended to assess your understanding of the rules of probability, the Theorem of...
This question is intended to assess your understanding of the rules of probability, the Theorem of Total Probability and Bayes' formula. You should be able to answer this question after working through Section 1 of Book 1. A manufacturer obtains supplies of a particular component from three different sources: 15%, 50% and 35% of its supplies are obtained from sources 1, 2 and 3. respectively. The percentages of components from sources 1, 2 and 3 that prove to be faulty...
Question 2 (10 marks) In this question you must state if you use any standard limits, continuity, l'Hôpital's rule, the sandwich theorem or any convergence tests for series. You do not need to justify using limit laws 2n n3 or explain why it does not exist. (a) Evaluate lim n (b) Determine whether each of the following converge: n+3 2n (i) 2 (3n) (ii) (n3)! n=1
Question 2 (10 marks) In this question you must state if you use any...
1. Consider the function -F5 sin(r) for r f(x) =2 for 1< 3 2-25 for 3 x2 -9x + 20 Evaluate the following limits You do not have to cite limit laws, but you must show how you arrived at your answer If a limit Does Not Exist, explain why. You should use oo or -oo where applicable Calculating the limit using L'Hopital's Rule will receive NO CREDIT. (a) lim f(x) r-+0 (b) lim f(x)= z-1 (e) lim f(z) (d)...
real analysis
1,3,8,11,12 please
4.4.3
4.4.11a
Limits and Continuity 4 Chapter Remark: In the statement of Theorem 4.4.12 we assumed that f was tone and continuous on the interval I. The fact that f is either stric tric. strictly decreasing on / implies that f is one-to-one on t one-to-one and continuous on an interval 1, then as a consequence of the value theorem the function f is strictly monotone on I (Exercise 15). This false if either f is...
Format requirement:
Question 3. E-6 Proof (Show Working) 10 points 249 Show that f:RR defined by f(x) is continuous at x = 7 using only r +3 cosa the epsilon-delta definition of continuity. Note that we want you to do it the hard way: you are not allowed to use the limit laws or the combination of continuous functions theorem or similar. You must give an 'e-δ style proof Solution: Let ε > 0 be given and choose δ =...
Do problems 1 and 3 please. Use any entries for the first
problem. Thank you.
1. (a) Make a table, rounding all entries to four decimal digits, to estimate the instantaneous rate of change of f(x) = x° at x = 1. Round your final answer to three decimal digits (b) Briefly describe how the entries in your table relate to the graph f(x)= x. In addition, briefly explain how your final estimate relates to the graph of f(x) =...
Problem 3. Prove Theorem 1 as tollows [Assume all conditions of the Theorem are met. In many parts, it will be useful to consider the sign of the right side of the formula-positive or negative- ad to write the appropriate inequality] (a) Since f"(x) exists on [a, brx) is continuous on [a, b) and differentiable on (a,b), soMean Value Thorem applies to f,on this interval. Apply MVTtof"m[x,y], wherc α zcysb. to show that ry)2 f,(x), İ.e. that f, is increasing...
Write ‘T' for true or ‘F' for false. You do not need to show any work or justify your answers for this question. The questions are 2 points each. (a) __If (xn) is a convergent sequence (converging to a finite limit) and f:RR is a continuous function, then (f (xn)) is a convergent sequence. (b) _If (xn) is a Cauchy sequence with Yn € (0,1) and f :(0,1) + R is contin- uous, then (f(xn)) is also a Cauchy sequence....
f(T) = 22 9 Instructions: • If you are asked for a function, enter a function. • If you are asked to find 2- or y-values, enter either a number or a list of numbers separated by commas. If there are no solutions, enter None. • If you are asked to find an interval or union of intervals, use interval notation. Enter { } if an interval is empty • If you are asked to find a limit, enter either...
Determine if the statement is True or False. You do not need to explain your choice. (T/F) a. Any two vectors can be added together. b. If I = c is not in the domain of f(x) and a <csb, then | slo) do f(1) dar is an improper integral (T/F) c. It is possible for a series (-1)*ax to converge and at to diverge. (T/F) d. The vectors u xv and v x u can never be equal. (T/F)...
This question is intended to assess your understanding of the rules of probability, the Theorem of Total Probability and Bayes' formula. You should be able to answer this question after working through Section 1 of Book 1. A manufacturer obtains supplies of a particular component from three different sources: 15%, 50% and 35% of its supplies are obtained from sources 1, 2 and 3. respectively. The percentages of components from sources 1, 2 and 3 that prove to be faulty...
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