# Thread: limits

1. ## limits

let f be defined as follows where a is not equal to 0.
f(x) = x^2-a^2 for x is not equal to a
and f(x) = 0, for x=a

which of the following are true about f?
I. lim from x to a f(x) exists
II. f(a) exists.
III. f(x) is continuous at x=a

2. ## Ok

Originally Posted by sandiego234
let f be defined as follows where a is not equal to 0.
f(x) = x^2-a^2 for x is not equal to a
and f(x) = 0, for x=a

which of the following are true about f?
I. lim from x to a f(x) exists
II. f(a) exists.
III. f(x) is continuous at x=a

I. and II. are correct...because we know the limit exists by how the question is worded...and we see that II. is correct becuase it states $\displaystyle f(a)=0$....and we see that three is incorrect because to have continuity at a point c $\displaystyle f(c)=lim_{x \to c}f(x)$ which is not the case here

3. Originally Posted by Mathstud28
[snip]we see that three is incorrect because to have continuity at a point c $\displaystyle f(c)=lim_{x \to c}f(x)$ which is not the case here
*Ahem* III is correct:

$\displaystyle \lim_{x \to a}f(x) = 0 = f(a)$ .....

4. ## Haha

Originally Posted by mr fantastic
*Ahem* III is correct:

$\displaystyle \lim_{x \to a}f(x) = 0 = f(a)$ .....
Of course I would forget the problem and do something like that...haha thanks for catching my careless mistake