MATH 1131/1141 Help (1 Viewer)

[Jonneeh]

Easy question i know but,

Suppose that f:R -> R is defined by f(x)=|x|

a) show that f is continuous at 0
b) is f continuous everywhere? Give brief reasons for your answer.

and what does (f : R-> R) mean.

 

[davidbarnes]

I think this is a limits question.

As 'R -> R' means as the variable (X) goes towards a point, i.e. it would be written as, as X -> 0 or as X -> infinity etc.

I hated that stuff.

At a guess I'd say f is continuous everywhere on the interval [0, infinity).

 

[tommykins]

if i remember correctly R->R just means placing a real number will result in a real number

 

[unsw-maths-guru]

Easy question i know but,

Suppose that f:R -> R is defined by f(x)=|x|

a) show that f is continuous at 0
b) is f continuous everywhere? Give brief reasons for your answer.

and what does (f : R-> R) mean.

1) f: R -> R just means that the function takes a real number x in and outputs a real number. (You could compare that to something like f: C -> R defined by f(z) = |z| which takes in a complex number z and outputs a real number (its modulus).)

2) f is continuous at a point a if lim(x -> a) f(x) = f(a).
The short answer to (a) then is to say that lim(x -> 0) f(x) = f(0). Do they tell you whether you need to prove the limit? I thought that they dropped the epsilon-delta stuff from 1st year so that seems unlikely?? Or do they want you to write
lim(x -> 0+) f(x) = lim(x -> 0+) x = 0
and
lim(x -> 0-) f(x) = lim(x -> 0-) (-x) = 0
and as these are equal the limit exists and equals zero?

3) For (b), the function is continuous everywhere. If a>0 then near a, f(x) = x which is continuous. If a < 0 then near a, f(x) = -x which is also continuous.

 

[Jonneeh]

Thanks guys
that's what i wrote anyways i just didn't know if it was the correct working out and what not, since there hardly any examples in the course book thing and there no worked solutions.

 

[hscstudent1]

I think this is a limits question.

As 'R -> R' means as the variable (X) goes towards a point, i.e. it would be written as, as X -> 0 or as X -> infinity etc.

I hated that stuff.

At a guess I'd say f is continuous everywhere on the interval [0, infinity).

lol man you practically failed maths, why are you answering maths questions

 

[kaz1]

go to SSS thrid floor red centre