continuity

1. Continuity Check of a 3 variables (D,H,L) function

hello everyone, I have a case I don't really know how to deal with. I have a function (objective function) of 3 variables (that represent the decision space) and a limited decision space as described in the picture attached. How can I check if the function is continuous over the entire limited...

Hello! We've been given homework on continuity and I tried solving one of the items but got a little stuck... I don't really know what else to do. Can someone please point me in the right direction? I also posted a picture of my attempt at solving it just in case I was actually doing the right...
3. Finding an approximation? (Continuity Correction?)

Hello everyone hope you're all having a good day, this question has been bugging me on a past paper I have been practicing for two days. The question is: The Colosseum in Rome can be divided into several thousand small sections.Suppose that the earthquake force that a section can withstand has...
4. Derivative of a differentiable function?

Let f(x) be a differentiable function. Then what are the conditions for which f'(x) is continuous and what are the conditions for which it is discontinuous? The derivative of a differentiable function can indeed be discontinuous... For example, g(x) = x2 sin(1/x) , for a nonzero x =...
5. Differentiability of functions

f(x)= b-ax if x is less than than or equal to 1 f(x) = a(x-2)^3 +x if x>1 1. Find values of a and b that make f differentiable 2. Find a set of values for a and b that make f continuous but not differentiable thanks! I did the problem myself and got a=-1/4 and b=1 for part 1, I'm not sure...
6. Question on differentiatialibility and continuity

I am reviewing all of my notes where we have a piecewise function, and I see everytime we check for differentiability, we check for continuity first. For example I will show you problem. I do not understand why do we check continuity first always, if the theorem holds that if it is...
7. Continuity proof

Hello All, thank you in advance for your help. My assigned proof is thus: Let I,J⊆ R be open intervals, and let f:I→R be a function. Suppose f is continuous. Let x∈f^(-1) J. Prove that there is some open interval K⊆ R such that x∈K∩I⊆f^(-1) J. This proof is stumping me. I can see that if I...
8. Continuity of a piecewise function

Find a and b such that f is continuous. f(x)=(x^2) x<-1, (ax+b) -1<x<2, (x^2) x>2
9. Continuity and Differentiable functions

Let ff be continuous and differentiable on the interval [a,b][a,b]. Assuming ff is bounded on the interval [a,b][a,b] and m=inf[a,b]f(x)m=inf[a,b]f(x), prove that there exists d∈[a,b]d∈[a,b] such that f(d)=mf(d)=m. You can use the fact that a function which is continuous on a closed interval is...
10. continuity of y = ((x^2)-4) / x-2

I was asked to determine whether the y = ((x^2)-4) / x-2 is continuous at x= 2 . The ans given is not . But , when I factrorise the upper part to become (x+2) and (x-2) , then I can cancel off x-2 , leaving y= x+2 , the graph of y= x+2 is certainly continuous at x=2 ....which is correct ?
11. Continuity of Piecewise-functions

My textbook has several interesting piecewise-defined functions concerning continuity but I have no idea where to begin. Say f(x) is a piecewise-defined function. Top part of f(x) = -2x+3, x< 0 Bottom part of f(x) = x^2, x >or= 1 Here are the instructions:Find the x-values (if any) at which f...
12. Absolute Value and Continuity

Find the x-values (if any) at which f is not continuous. Which of the discontinuities are removable? f(x) = |x - 3|/(x - 3) I don' t know where to start.
13. Continuity of Functions

Find the x-values (if any) at which f is not continuous. Which of the discontinuities are removable? f(x) = 3x - cosx I don' t know where to start.
14. Continuity

We say a function is continuous if when drawing the graph can be done without lifting the pencil of the paper. What is the mathematical definition of continuity? What three rules must take place in order for a function to be continuous?
15. Sampling - Binomial/Normal + Continuity Correction

Hi, I have been trying to do this question: The proportion of faulty plastic cups made by a factory machine is 0.08. The cups, including faulty ones, are packed in boxes of 100. About 4000 cups are required for an outdoor concert and the manager orders 44 boxes. Find the probability that these...
16. uniform continuity at sinx

How can I prove that this function is not uniform continuous at R \mathop {\sin (e}\nolimits^x ) I dont know how to solve this . even how to begin. I didnt learn l'hopital rule yet.
17. Limits Continuity

I'm creating my cheat sheet for my final next week and I just wanted to check if I have things right... Calculus Notes Chapter 2: 1.) Understand the intuitive meaning of a limit. My Question: Does this have to do with epsilon and delta? 2.) Identity and explain when a limit does not exist...
18. Prove continuity

7. BONUS (4 points) Let f be the function defined by: . . . . .f(x)={x2−x2 if x is rational if x is irrational Is f continuous at x = 0? If so, prove it. If not, prove that it is not.
19. Continuity of inverse function at endpoints

Hello! *Let $f$ be a strictly increasing continuous function on a closed interval $[a, b]$, let $c = f(a), d = f(b)$, and let $g:[c, d] → [a, b]$ be its inverse. Then $g$ is a strictly increasing continuous function on $[c, d]$.* How can it be shown that $g$ is continuous at its endpoints...
20. Continuity promblem

Find all values of x at which f(x) fails to be continuous. F(x) = 6/(1-sin2x)