# Decide whether the following functions are continuous at a=0

1. Jan 13, 2009

### Fairy111

1. The problem statement, all variables and given/known data

Decide whether the following functions are continuous at a=0

2. Relevant equations

f(x)=x^2 if x<0 and f(x)=sinx if x>=0

3. 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.

2. Jan 13, 2009

### Hootenanny

Staff Emeritus
Re: continuity

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.

3. Jan 13, 2009

### Fairy111

Re: continuity

ok, thankyou.

So im looking at the left hand part of the parabola of x^2, which is when x<0.
It stops at x=0, im not really sure what to say about the continuity.

4. Jan 13, 2009

### danago

Re: continuity

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

5. Jan 13, 2009

### Hootenanny

Staff Emeritus
Re: continuity

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

6. Jan 13, 2009

### HallsofIvy

Staff Emeritus
Re: continuity

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

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