Determine the limit of the function (x^2 + 1)/(x + 1)^2 , x--> + infinite

First, we'll expand the square from the denominator, using
the
formula:

 (a+b)^2=a^2+2ab+b^2

We'll
put a = x and b =
1.

(x+1)^2=x^2+2x+1

In order
to calculate the limit of a rational function, when x tends to +inf., we'll divide both,
numerator and denominator, by the highest power of x, which in this case is
x^2.

We'll have:

lim (x^2 +
1)/(x+1)^2 = lim (x^2 + 1)/lim (x^2+2x+1)

lim x^2*(1 +
1/x)/lim x^2*(1 + 2/x + 1/x^2)

After reducing similar
terms, we'll get:

lim (x^2 + 1)/(x+1)^2 =
(1)/(1+0)

lim
(x^2 + 1)/(x+1)^2 = 1