Understanding Continuity and Intervals for Limits in Functions

[noobie!]

i would like someone to clear my doubts by explaining how it actually works..limits is one of the chapter i fear about it cause I am quite blur with it..so i do need someone help me;v this que..given f(x)=1/x^3 what r the intervals for function continuous ?how to solve it?thanks :)

 

[lurflurf]

f is continuous when
lim_{h->0} [f(x+h)-f(x)]=0
also composition of continuous funtions are continuous
x^3 is everywhere continuous
where is 1/x continuous?

 

[noobie!]

f is continuous when
lim_{h->0} [f(x+h)-f(x)]=0
also composition of continuous funtions are continuous
x^3 is everywhere continuous
where is 1/x continuous?

u meant composite of continuous function could also be a continuous for x^3?bt the limit is not given?!so what will be the interval for the function?how to differentiate between them and i still don't really get your point;i'm so sorry!

 

[lurflurf]

let g(x)=x^3
write f(x)=1/x^3
as
f(g(x))=g(1/x)=(1/x)^3
g(x) is continuous for all real numbers (show this)
so f is continuous at a if and only if 1/x is continuous at a.
Where is 1/x continous?

Start by giving the domain of 1/x
A function cannot be continuous where it is undefined.

 

[noobie!]

let g(x)=x^3
write f(x)=1/x^3
as
f(g(x))=g(1/x)=(1/x)^3
g(x) is continuous for all real numbers (show this)
so f is continuous at a if and only if 1/x is continuous at a.
Where is 1/x continous?

Start by giving the domain of 1/x
A function cannot be continuous where it is undefined.

hmm,then i think i get your point..anyway thanks alot...