Homework Answers
![Giren sak hint NS Here s c (0,1] =B, say Therefore sc B = [0, 1]. 32 First we prove that o in Sol a limit point of s. Les Ey](http://img.homeworklib.com/questions/936957a0-bda3-11ea-8ab5-cb6506620b9f.png?x-oss-process=image/resize,w_560)
Add Answer to:
(complete the proof. Hint: Use the Squeeze Theorem to show that lima = L.) 3- For...
(Proof of the Squeeze Theorem for Functional Limits). Let f.g, h: A R be three functions...
(Proof of the Squeeze Theorem for Functional Limits). Let f.g, h: A R be three functions satisfying f(x) < 9(2) < h(r) for all re A, and suppose c is a limit point of A and lim; cf(x) = L and lim -ch() = L. Prove that lim.+c9(x) = L as well.
Please help me solve 3,4,5 3- For all n € N, let an = 1. Let...
Please help me solve 3,4,5
3- For all n € N, let an = 1. Let S = {an in€ N}. 3-1) Use the fact that lim - = 0 and the result of Exercise 1 to show that 0 ES'. Ron 3-2) Use the result of Exercise 2 to show that S = {0}. 4- Prove that 4-1) N' = 0. 4-2) Q =R. 5- Recall that a set KCR is said to be compact if every open cover...
#23 22, Use the definition of limit to prove Theorem 3.5. 23. Use Theorem 3.5 to...
#23
22, Use the definition of limit to prove Theorem 3.5. 23. Use Theorem 3.5 to prove that lim x? cost(1/x)-0. In addition, give a proof of th result without using Theorem 3.5. THEOREM 3.5 Squeeze Theorem for Functions Let I be an open interval that contains the point c and suppose that f, g, except possibly at the point c. Suppose that g(x) s f(a) s h(x) for all x in I If limn g(x)-L = lim h (x),...
10. Use the Fundamental Theorem of Calculus to provide a proof of Theorem 8.4 under the additiona...
10. Use the Fundamental Theorem of Calculus to provide a proof of Theorem 8.4 under the additional assumption that each fis continuous on I la, b).(Hint: For x in la, b.o)If f g uniformly on [a, b], then Theorem 8.3 implies that im f.(x) f (x8. It follows that frpuintwise on la, b), where F(x) -lim frCro) + .By Theorem 6.12, F()-x) on la,b). Now show that f uniformly on la, b].] F heorem 8.4 Suppose that neN is a...
Can you solve No.6 6. Let (a.)and b) be bounded sequences in R .a. Prove that lima. +İimb, siim (a, + b.) s ima, + İim br b. Prove that lim (-a)lima . Given an example to show that equality need n...
Can you solve No.6
6. Let (a.)and b) be bounded sequences in R .a. Prove that lima. +İimb, siim (a, + b.) s ima, + İim br b. Prove that lim (-a)lima . Given an example to show that equality need not hold in (a) If o, and b, are positive for all n, prove that lim (a)s(im a)mb). provided the product on the right is 7. not of the form 0 oo. b. Need equality hold in (a)?
6....
2. Let (En)acy be a sequence in R (a) Show that xn → oo if and only if-An →-oo. (b) If xn > 0 for...
#s 2, 3, 6
2. Let (En)acy be a sequence in R (a) Show that xn → oo if and only if-An →-oo. (b) If xn > 0 for all n in N, show that linnAn = 0 if and only if lim-= oo. 3. Let ()nEN be a sequence in R. (a) If x <0 for all n in N, show that - -oo if and only if xl 0o. (b) Show, by example, that if kal → oo,...
(1) Use the Squeeze Theorem to show that limx-ox* cos(207x) = 0. Give all your reasons....
(1) Use the Squeeze Theorem to show that limx-ox* cos(207x) = 0. Give all your reasons. (2) Use ONLY THE DEFINITION (Either f'(a) = lim - 12)={@ or f'(a) = lima_vo f(a+h)-f(@)) to find the derivative of f(x) = 2x +1 at x = 3. (3) Findf, if f'(x) = 2+1 +20 +€* – sin 2 and f(0) = In(5). (4) Differentiate y = x*
If you use a statement or theorem, please proof it first or explain how to proof...
If you use a statement or theorem, please proof it first or
explain how to proof it, thanks in advance
ne Z? 1.13 Let p > 3 be a prime number. Show that p=6k+ 1 or p = 6k +5 for some k e Z. - - L OL. 1 . ait diricible bu
In the following problem, we will work through a proof of an important theorem of arithmetic. Your job will be to read the proof carefully and answer some questions about the argument. Theorem (The Di...
In the following problem, we will work through a proof of an
important theorem of arithmetic. Your job will be to read the proof
carefully and answer some questions about the argument. Theorem
(The Division Algorithm). For any integer n ≥ 0, and for any
positive integer m, there exist integers d and r such that n = dm +
r and 0 ≤ r < m. Proof: (By strong induction on the variable n.)
Let m be an arbitrary...
6. Suppose that {x,] is a sequence of positive numbers and limA = a Show that...
6. Suppose that {x,] is a sequence of positive numbers and limA = a Show that if L> 1 then lim x =00, and if L < 1 lim x = 0 n+02 b. Construct a sequence of positive numbers {x,} such that lim * = 1 and the sequence {x} diverges. c. Let k E N and a > 1 Show that lim = 0. O LIVE
(Proof of the Squeeze Theorem for Functional Limits). Let f.g, h: A R be three functions satisfying f(x) < 9(2) < h(r) for all re A, and suppose c is a limit point of A and lim; cf(x) = L and lim -ch() = L. Prove that lim.+c9(x) = L as well.
Please help me solve 3,4,5
3- For all n € N, let an = 1. Let S = {an in€ N}. 3-1) Use the fact that lim - = 0 and the result of Exercise 1 to show that 0 ES'. Ron 3-2) Use the result of Exercise 2 to show that S = {0}. 4- Prove that 4-1) N' = 0. 4-2) Q =R. 5- Recall that a set KCR is said to be compact if every open cover...
#23
22, Use the definition of limit to prove Theorem 3.5. 23. Use Theorem 3.5 to prove that lim x? cost(1/x)-0. In addition, give a proof of th result without using Theorem 3.5. THEOREM 3.5 Squeeze Theorem for Functions Let I be an open interval that contains the point c and suppose that f, g, except possibly at the point c. Suppose that g(x) s f(a) s h(x) for all x in I If limn g(x)-L = lim h (x),...
10. Use the Fundamental Theorem of Calculus to provide a proof of Theorem 8.4 under the additional assumption that each fis continuous on I la, b).(Hint: For x in la, b.o)If f g uniformly on [a, b], then Theorem 8.3 implies that im f.(x) f (x8. It follows that frpuintwise on la, b), where F(x) -lim frCro) + .By Theorem 6.12, F()-x) on la,b). Now show that f uniformly on la, b].] F heorem 8.4 Suppose that neN is a...
Can you solve No.6
6. Let (a.)and b) be bounded sequences in R .a. Prove that lima. +İimb, siim (a, + b.) s ima, + İim br b. Prove that lim (-a)lima . Given an example to show that equality need not hold in (a) If o, and b, are positive for all n, prove that lim (a)s(im a)mb). provided the product on the right is 7. not of the form 0 oo. b. Need equality hold in (a)?
6....
#s 2, 3, 6
2. Let (En)acy be a sequence in R (a) Show that xn → oo if and only if-An →-oo. (b) If xn > 0 for all n in N, show that linnAn = 0 if and only if lim-= oo. 3. Let ()nEN be a sequence in R. (a) If x <0 for all n in N, show that - -oo if and only if xl 0o. (b) Show, by example, that if kal → oo,...
(1) Use the Squeeze Theorem to show that limx-ox* cos(207x) = 0. Give all your reasons. (2) Use ONLY THE DEFINITION (Either f'(a) = lim - 12)={@ or f'(a) = lima_vo f(a+h)-f(@)) to find the derivative of f(x) = 2x +1 at x = 3. (3) Findf, if f'(x) = 2+1 +20 +€* – sin 2 and f(0) = In(5). (4) Differentiate y = x*
If you use a statement or theorem, please proof it first or
explain how to proof it, thanks in advance
ne Z? 1.13 Let p > 3 be a prime number. Show that p=6k+ 1 or p = 6k +5 for some k e Z. - - L OL. 1 . ait diricible bu
In the following problem, we will work through a proof of an
important theorem of arithmetic. Your job will be to read the proof
carefully and answer some questions about the argument. Theorem
(The Division Algorithm). For any integer n ≥ 0, and for any
positive integer m, there exist integers d and r such that n = dm +
r and 0 ≤ r < m. Proof: (By strong induction on the variable n.)
Let m be an arbitrary...
6. Suppose that {x,] is a sequence of positive numbers and limA = a Show that if L> 1 then lim x =00, and if L < 1 lim x = 0 n+02 b. Construct a sequence of positive numbers {x,} such that lim * = 1 and the sequence {x} diverges. c. Let k E N and a > 1 Show that lim = 0. O LIVE
Most questions answered within 3 hours.
-
Consider the reaction, C3 H8 + O2 --> CO2 + H2O. How many
moles of O2...
asked 19 minutes ago -
You and your opponent both roll a fair die. If you both roll the
same number,...
asked 37 minutes ago -
In a study of the accuracy of fast food drive-through orders,
Restaurant A had 257 accurate...
asked 36 minutes ago -
Identify and describe in detail the four categories of
institutions that could be included in a...
asked 42 minutes ago -
In python
class Customer:
def __init__(self, customer_id, last_name, first_name, phone_number, address):
self._customer_id = int(customer_id)
self._last_name =...
asked 50 minutes ago -
What is an example of a limitation in implementing a new
ERP system and how it...
asked 45 minutes ago -
In a section of 9.7cm of an artery with a radius of 2.6mm there
is a...
asked 46 minutes ago -
the two carboxylic acid groups of aspartic acid have different
acidities with pKa values of 2.1...
asked 50 minutes ago -
Would CuCO3 aqueous salt combined with calcium chloride
form a solid precipitate? If so, what would...
asked 49 minutes ago -
How do ECM Solutions assist in embedding a culture of continuous
improvement in an organization? (Project...
asked 1 hour ago -
Directions
These directions introduce the idea of Essential Questions.
Since this may be a new concept...
asked 1 hour ago -
1.b. Fiscal policy is said to suffer from ‘crowding out’.
Explain what this means and why...
asked 1 hour ago