<p>i have an ap calc bc question...</p>
<p>i am supposed to find the constant a such that the function is continuous on the entire real line:</p>
<p>g(x) = (x^2 - a^2) / (x-a), given that x is not equal to a
8 , given that x = a</p>
<p>could someone please give me the answer to this? i thik i've got it, but i'm not sure.</p>
<p>well first of all you need to know the definition of continuity</p>
<p>lim f(x) = f(c)
x->c
(All the following values must exist.)</p>
<p>Well, you know what f(c) is when c = a and when c does not equal a</p>
<p>lim f(x) = (c^2 - a^2) / (c-a) = f(c), for all c not equal to a
x->c</p>
<p>Thus, the problem lies with when x = c = a
You are given that f (c) = 8</p>
<p>Thus, you must find x such that lim f(x) = 8
x->c
lim f(x) = (c^2 - a^2) / (c - a) = c + a (Remember FOIL?)
x->c</p>
<p>c + a = 8
x + a = 8
2a = 8
a = 4</p>