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

(Talking)

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- Apr 12th 2008, 07:55 PMsandiego234limits
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

(Talking) - Apr 12th 2008, 08:00 PMMathstud28Ok
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

- Apr 12th 2008, 09:19 PMmr fantastic
- Apr 12th 2008, 09:41 PMMathstud28Haha