continuous

Can you help the following problems? 1) Let f, g be defined on R and let c in R. Suppose that lim f = b and that g is continuous at b. show that lim g 0 f = g(b) Note: R: real numbers g 0 f means composition of f and g 2) Let A = [0, 1) U (1,2]. Let B = [0, 1] U [2, 3]. Does the conclusion of the maximum-minimum ...continues

Max-Min theorem

Recall: Max-Min theorem: Let f: [a, b] -> R (real numbers) be continuous on [a, b]. Then f has an absolute maximum and an absolute minimum on [a, b] Please see attachment for problem. Thanks in advance for your help

Mean, Median and Mode

2. Find the mean, median, and mode of the following data set: 5 15 9 22 67 42 2 72 81 53 6 70 41 9 42 23

finite or countable collection of disjoint open intervals

(Complete problem found in attachment)

Sequences and Subsets

(See attached file for full problem description)

prove sequences - 2 problems

(See attached file for full problem description) --- 1) a. Let with . If is a measurable subset of R, prove that and are measurable. b. let E =[0,1]Q. Prove that E is measurable and (E)=1. c. let P denote the cantor set in [0,1]. Prove that 2) If E R, prove that ther exists a sequence { } ...continues

Measurable functions

1) a. If g is measurable on [a, b] with g(x) 0 for all x [a, b], prove that 1/g is measurable on [a, b]. b. prove that every continuous real- valued function f on [a, b] is measurable. c. if f is differentiable on [a, b], prove that f' is measurable on [a, b]

see attachement

(See attached file for full problem description) --- 1) a. Let f be defined on [a, b] by f(x) prove directly that f is measurable b. let E be measurable subset of R, and let f be measurable function on E Define the function f and f on E as follows: f (x) = max { f(x), 0}, and f (x) = max{ -f(x), 0}, 1b. prove direc ...continues

Statistics

The average numbers of home runs hit by the Boston Red Sox per game are: 2 divided by 3 = .66 5 divided by 2 = 2.5 6 divided by 1 = 6 7 divided by 0 = 0 Is that correct using the weighted approach?

A thin glass pipe with internal diameter of 3mm was probed into the heart tissue (membrane) and air pressure was applied

A thin glass pipe with internal diameter of 3mm was probed into the heart tissue (membrane) and air pressure was applied... See attached file for full problem description.