returns the product:
x^4-16 =
(x^2-4)(x^2+4)
We notice that the 1st factor is also
a difference of squares that returns the product:
x^2-4 =
(x-2)(x+2)
We'll re-write the
function:
(x^4-16)/(x-2) =
(x-2)(x+2)(x^2+4)/(x-2)
We'll
simplify:
(x^4-16)/(x-2) =
(x+2)(x^2+4)
We'll evaluate the limit the
fraction:
lim (x^4-16)/(x-2) = lim
(x+2)(x^2+4)
We'll replace x by
2:
lim (x+2)(x^2+4) = (2+2)(4+4) = 4*8 =
32
The value of the limit, if x
approaches to 2, is lim (x^4-16)/(x-2) = 32.
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