What is the limit of the function sin x/squareroot(x^2+1), x->+infinite?

We cannot calculate the limit of sine function if
x-> +infinite.

We'll calculate the function based on
the property of product of 2 functions, if the limit of one function is 0 and the other
function is bordered.

By definition, the sine function is
limited by the values -1 and 1.

|sin
x|=<1

Now, we'll calculate the limit of the fraction
1/sqrt(x^2+1):

lim 1/sqrt(x^2+1) = 1/infinite =
0

We'll write the given function as the product of 2
functions:

lim [1/sqrt(x^2+1)]*(sin x) = 0,
if x->infinite