Decide whether the following functions are continuous at a=0

[Fairy111]

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.

 

[Hootenanny]

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.

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]

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.

 

[danago]

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.

Do you know the formal definition of continuity? What conditions must be met?

 

[Hootenanny]

HINT: Looking at the question, the first thing to consider would be whether a=0 belongs to the domain of f ...

 

[HallsofIvy]

Good point, Hootenanny, but I am wodering if the OP didn't just misstate the definition of f.