Evaluate limit x/(x+1)^2, x->+infinity.

First, we'll expand the square from the denominator, using the formula (a+b)^2=a^2+2ab+b^2.

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

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

After reducing similar terms, we'll get:

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