2. (10 marks) Prove that f(x) = 6 ln(x – 11) is not uniformly continuous on...
2. (10 marks) Prove that f(x) = 5 ln(x – 7) is not uniformly continuous on (0,00).
10 marks) Prove that f(x) = 6 ln(x – 11) is not uniformly continuous on (0,0).
(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 -...
2. a. Prove that f(x) = V22 - 13 is uniformly continuous on the interval (7,0). b. Prove or disprove: f(x) = V x2 - 13 is not uniformly continuous on the interval ( 13, 7). c. Prove or disprove: If a > 13, f(x) = 32-13 is uniformly continuous on the interval (a,
Prove that f(x) = is uniformly continuous on (1,00) and not uniformly continuous on (0,1). (19 pts)
2) Drove that f(x) = 6 lom (x-11) is uniformly continuous on (0, ) not
10. (a) 5pts] Prove that if f is piecewise continuous on [0,00) and satisfies the growth is, f(t) Me for restriction that some constants M k>0 on [0,00), then lim f(t)]=0 (b) [5pts] Find the inverse transform of s+1 F(6) s) = ln (c) [8pts] Find a solution of ty"+2y-ty= 0, y(0)=1, y (1)= Hint) You may need to use (a) and (b). 10. (a) 5pts] Prove that if f is piecewise continuous on [0,00) and satisfies the growth is,...
Prove that f(x) is uniformly continuous on [0 inf) if lim f(x) = 0.
(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 (?),...