Let E be a nonempty subset of R and f:E-->R. State the definition f is uniformly continuous on E. Prove f(x) =x^2 is uniformly continuous on the interval[0,1].

Uniform continuity is investigated. The solution is detailed and well presented. The response received a rating of "5/5" from the student who originally posted the question.

... values as well as decimal values, and therefore, T is a continuous random variable ... distribution, then the lifetimes of the bulbs must vary uniformly between the ...

... Suppose # is defined on a finite interval I and ′# is continuous on I. Suppose ′# converges uniformly on I. Suppose moreover that there exists at least one ...

... 2 Let X be a continuous random variable with the pdf f(x) = 42x5(1-x) 0<x<1 and let Y=X3. Suppose u=.145 is a random number generated from the uniform (0,1 ...

... properties: a) The constant function belongs to A. b) If c) if d) if Then any continuous function K to R can be uniformly approximated on K by functions in A. ...

QUESTION 1 A continuous uniform distribution U(100,200) will have the same standard deviation as a continuous uniform distribution U(200,300). True False. ...

... 8. Prove that f(x) = x^1/2 is uniformly continuous on [0,infinity). ... ab. 8. Prove that f ( x) = x is uniformly continuous on [0, ∞). 1/ 2. Solution: ...

... The chief mechanic has determined that the time to paint automobiles is uniformly distributed and that the required time ranges between 45 minutes to 1 1/2 ...

... 5) It is easy to see that this is a maximum, since fk = continuous, positive and ( 6) Therefore: ( 7) and the sequence fk is not uniformly convergent to zero ...