The discussion revolves around determining the continuity of a piecewise function at the point a=0. The function is defined as f(x)=x^2 for x<0 and f(x)=sinx for x>=0.
The discussion is ongoing, with participants providing hints and clarifications about the definition of continuity and the importance of the point a=0. There is an exploration of whether the original poster may have misstated the function's definition.
There is some uncertainty regarding the formal definition of continuity and the conditions that must be met for the function at the specified point. Participants are also considering the domain of the function in relation to the point a=0.
a is simply the point under consideration. More verbosely the question could ask "Let a=0. Decide whether the following functions are continuous at x=a ...". So, you simply need to examine the continuity of the f(x) at the origin.Fairy111 said:Homework Statement
Decide whether the following functions are continuous at a=0
Homework Equations
f(x)=x^2 if x<0 and f(x)=sinx if x>=0
The Attempt at a Solution
I don't really understand where the 'a' comes in the functions? Some help/hints as to how to start off this question would be much appreciated.
Fairy111 said:ok, thankyou.
So I am looking at the left hand part of the parabola of x^2, which is when x<0.
It stops at x=0, I am not really sure what to say about the continuity.