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(a) PROOF:
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(b) We DISPROVE the statement as follows:
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(c) We PROVE the statement as follows:
2. a. Prove that f(x) = V22 - 13 is uniformly continuous on the interval (7,0)....
Prove that f(x) = is uniformly continuous on (1,00) and not uniformly continuous on (0,1). (19 pts)
2. (10 marks) Prove that f(x) = 5 ln(x – 7) is not uniformly continuous on (0,00).
(10 marks) Prove that fx=6ln(x-11) is not uniformly continuous on (0,∞) Х Enable Editing X i PROTECTED VIEW Be careful—files from the Internet can contain viruses. Unless you need to edit, it's safer to stay in Protected View. LAAM Yuuuus = (x2-x-2 1. (10 marks) Let f(x) (x2-4) if x # +2 с if x = 2 Find c that would make f continuous at 1. For such c, prove that f is continuous at 1 using an ε -...
(10) Prove that if (fn) is a sequence of uniformly continuous functions on the interval (a, b) such (a, b), then f is also uniformly continuous on (a, b) that f funiformly on en dr 0. (11) Show that lim n-+o0 e (10) A G.. 11d
Urgent help needed in Math Problems ! Thanx 3. Prove that f(x)=1/(1-) is not uniformly continuous for 12 <1. 4. Show that the function f(x) = 1/22 is not uniformly continuous for 0 < Rez <1/2 but is uniformly continuous for 1/2 < Rez < 1. 6. Discuss continuity of (Rez)? (Im ) if : +0 if 20 f(2)= |z| 2 my 0 if = 0 at the all points of C. 7. Find the following limits: (a) lim (?),...
Let f:D + R be a function. (a) Recall the definition that f is uniformly continuous on D. (You do not need to write this down. This only serves as a hint for next parts.) (b) Use (a) and the mean value theorem to prove f(x) = e-% + sin x is uniformly continuous on (0, +00). (c) Use the negation of (a) to prove f(x) = x2 is not uniformly continuous on (0,0).
2. (10 marks) Prove that f(x) = 6 ln(x – 11) is not uniformly continuous on (0,00)
Prove that f(x) is uniformly continuous on [0 inf) if lim f(x) = 0.
8. *** Prove that f(x) = ? is not uniformly continuous on (0,0). Remark: Recall that we proved in class that f(0) = .za is not uniformly continuous on (0,0). I remind you of this result in case it helps you think about how to approach this exercise.
Use the definition of uniform continuity to prove that f(x)is uniformly continuous on , 00