What is the limit of f(x)/x^4 if x goes to infinite and f(x)=(x-1)(x-3)(x-5)(x-7) ?

We'll force the x factor in each pair of brackets of f(x),
such as:

f(x) = x^4*(1 - 1/x)*(1 - 3/x)*(1 - 5/x)*(1 -
7/x)

We'll re-write the
limit:

lim f(x)/x^4 = lim x^4*(1 - 1/x)*(1 - 3/x)*(1 -
5/x)*(1 - 7/x)/x^4

We'll simplify and we'll
get:

lim f(x)/x^4 = lim (1 - 1/x)*(1 - 3/x)*(1 - 5/x)*(1 -
7/x)

Since the limit of each fraction 1/x ; 3/x ; 5/x ;
7/x, approaches to zero, when x approaches to infinite, we'll
get:

lim f(x)/x^4 = (1 - 0)*(1 - 0)*(1 - 0)*(1 -
0)

lim f(x)/x^4 =
1

The requested limit of the function
f(x)/x^4, if x approaches to infinite, is lim f(x)/x^4 =
1.