Find the limit of ( 2n4 - 15 ) / ( 6n4 + 17 ) as n gets increasingly larger.
Divide every term in the numerator and denominator by n4:
[ 2n4 / n4 - 15 / n4 ] / [ 6n4 / n4 + 17 / n4 ]
= [ 2 - 15 / n4 ] / [ 6 + 17 / n4 ]
As n gets very large both 15 / n4 and 17 / n4 get very small; they approach zero.
So, this approaches [ 2 - 0 ] / [ 6 + 0 ] = 1/3.