sin(x)/x = 1 when x approaches infinity. Direct substitution of x=0 gives the indeterminate form 0/0.
The limit of an indeterminate form can be any number. For instance
kx/x= 0 , |x|/x2= &inf; as x tends towards infinty.
Many indeteminate forms can be evaluated with basic algebra.
If this is not possible l’Hôpital’s rule is the solution.
It states that the limit of an indeterminate form equals the limit of the dervative of the nominator and denominator of the indeterminate form.