What is the limit of #(2x+3)/(5x+7)# as x goes to infinity?
Notice that the degree of the numerator and the denominator are
the same i.e: 1, for this and all the similar scenarios the limits is
simply the ratio of the leading coefficients of top to bottom:
#lim_(x->oo) (2x + 3)/(5x + 7) = lim_(x->oo) (2color(red)(cancel(color(black)(x))))/(5color(red)(cancel(color(black)(x))))#
#= lim_(x->oo) 2/5#