8. *** Prove that f(x) = ? is not uniformly continuous on (0,0). Remark: Recall that...
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).
10 marks) Prove that f(x) = 6 ln(x – 11) is not uniformly continuous on (0,0).
Prove that f(x) = is uniformly continuous on (1,00) and not uniformly continuous on (0,1). (19 pts)
(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 -...
b) i. Using e-8 definition show that f is continuous at (0,0), where f(x,y) = {aš sin () + yś sin () if xy + 0 242ADES if xy = 0 ii. Prove that every linear transformation T:R" - R" is continuous on R". iii. Let f:R" → R and a ER" Define Dis (a), the i-th partial derivative of f at a, 1 sisn. Determine whether the partial derivatives of f exist at (0,0) for the following function. In...
Prove that f(x) is uniformly continuous on [0 inf) if lim f(x) = 0.
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,
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 (?),...
a) Prove that for all x, y≥0 we have |√x−√y|≤√|x-y|. (b) Prove that f(x)=√x is uniformly continuous on [0,∞).
Let f(x) = x^(1/3) with domain (0,infinity). Prove, by
epsilon-delta language, that f is continuous at c in an element of
(0, infinity).
2. Let f(0) = 25 with domain (0,00). Prove, by the e-8 language, that f is continuous at CE (0,0)