Answer: We can factor the numerator and denominator of the expression as the difference of squares:
(x^2 - a^2) = (x - a)(x + a)
(x^4 - a^4) = (x^2 - a^2)(x^2 + a^2)
Substituting these into the limit expression, we get:
lim x→a [(x^2-a^2)/(x^4-a^4)]
= lim x→a [(x - a)(x + a) / (x^2 - a^2)(x^2 + a^2)]
We can simplify this expression by canceling out the common factor of (x - a) in the numerator and denominator:
lim x→a [(x + a) / (x^2 + a^2)]
Now, we can evaluate the limit by direct substitution, since the expression is continuous at x=a:
lim x→a [(x + a) / (x^2 + a^2)] = (a + a) / (a^2 + a^2) = 2a / 2a^2 = 1/a
Therefore, the limit of [(x^2-a^2)/(x^4-a^4)] as x approaches a (where a cannot equal 0) is 1/a.