# continous

1. ### strictly increasing function continous only at irrationals

hi! I'm looking for a strictly increasing function on I = [0, 1] that is continuous only at the irrational numbers in I. After some thought, I came up with the following arrangement. Enumerate the rational numbers in I as such: q_1, q_2, q_3, ... , q_n (with n a natural number) such that...
2. ### increasing, continous function on open interval

My attempt to prove (=>): Fix x in I. Since I is open, there is a ball of radius r>0 about x, so there points on the left and points on the right of x that belong to I. Fix the radius r. f is continuous and monotone on I; continuous and monotone on (x-r, x+r) which is bounded. [Using the...
3. ### preimage of a continous function is an interval

To prove: a continuous real-valued function (f) defined on set S has an image (S') that is an interval then S must be an interval. Tools: definition of continuity, definition of a connected set, connected set in R is an interval, If S' is not a singleton; if f(a), f(b) \in S' such that f(a)...
4. ### Continuity

Please, please please help me with this questions. Really struggling as i have been off uni ill for over a week now and missed alot of classes to make it worse this assesment is due in asap!! :( Many thanks, Hanna. x
5. ### Continous function Question

f(x) =(x+1)cotx be continuous at x=0 , then f(0)=? I think answer is 0 answer may be 0,1/e,e or none of these I am confused what should be the answer explain me the given answer Thanks in advance
6. ### regluated and continous function example

could someone give me the example that the function is: A) regulated and discontinuous B)not regulated and discontinous
7. ### f(x) continuous at c

Please Help!! Prove that if c is irrational f(x) is continuous at c. I would appreciate any type of hints or just where to start.
8. ### continous function

f(x)=e-1/x2 if x is not =0 =0 if x=0 then f is continuous. how it can be proved.
9. ### continous

if h(x)=0 if x is irrational no. h(x)=1/n if x is the rational number m/n(in lowest terms) h(0)=1 how it is proved that the function 'h' is continous only for irrational no. on [0,1] ? thank u
10. ### Continous compounding question

Hello all, I am working out a question at the moment and im not too sure if it is write or wrong. Hope someone can help thanks!! the question goes like this: A loan of 100K is taken out and n.interest is 8 percent. Firstly i found that if the loan is to repaid within 12 years the answer i...
11. ### Show a function is continous

Im not sure how to do this question because it is slightly different (there isnt a term like x^2 - 5x +2 etc.. but this is just h(x) and f(x). Thanks.. ImageShack® - Online Photo and Video Hosting
12. ### continous in the complex

How do i prove sin z is continuous in the complex region? Thanks Adam
13. ### What is the relationship between a and b so that f(x) is a continous function?

Given f(x) = 3x - a x (less than and equal to) -2 (x^2) - b x (greater than) -2
14. ### Continous function (prove)

I am trying to prove that \sqrt{id_\mathbb{R}} function is continous. Any help would be appreciated.
15. ### Continous Question

I need help on this problem: Also please explain how to do it. I started out by graphing the first function but not sure how to do the others/what its asking for.
16. ### Uniformly continous functions

PLZZZZZ SOVE DIS WID XPLANATION . . if f : R tO R is a cts funtion s.t f(x) tends to 0 as x tends to infinity show that f is unformly cts?
17. ### continous piece wise function

Create a continuous function f(x) on the interval [-4, 4] by drawing its graph which meets these conditions; f (0) = 2, f '(2) = 0, f '(-2) {is undefined, f "(0) = 0, f "(-1) is undefined. There is a point of inflection when x = 1 and a minimum at x = -2/3. The limit of f(x) as x approaches 4...
18. ### Continous function in topologies

f: (R,T_u) \rightarrow (R,T_{cof}) defined by f(x)=\left\{ \begin {array}{cc} -1 ,& \mbox x\in Q \\ 1 , &\mbox x\in Q^c \end {array}\right. is this function continuous, and is this function closed I found it closed and not continuous am I right ? Thanks in advance
19. ### Sufficient condition for Existence of continous retraction

If f maps X to X continuously and the range of f is A (subset of X) then is this sufficient to show that there exist a continuous retraction from X to A? If so, how can this be proven? If not, any counterexamples? Notes: This is the topological continuity I am speaking of. Also a I am using...
20. ### Finding the points where a function is continous

Find the set of all points of continuity for: f(x,y) = ln(\frac{x-y}{x^2+y^2}) i know that the domain is whenever ln is positive, so its whenever x-y>0 , x>y is it continuous on all points of the domain? also is it considered continuous on the edges of the surface? thanks