How do you find the slant asymptote of #f(x)=( 21 x^2 ) / ( 3 x + 7)#?

1 Answer
Jul 6, 2016

Answer:

#y = 7x#

Explanation:

#f(x)=( 21 x^2 ) / ( 3 x + 7)#

you ask specifically about slants wcih means we consider #x to pm oo#

# lim_{x to pm oo} ( 21 x^2 ) / ( 3 x + 7)#

#= lim_{x to pm oo} ( 21 x ) / ( 3 + 7/x)#

and # lim_{x to pm oo} ( 3 + 7/x) = 3#

so we can identify #y = 21/3 x = 7x# as a slant asymptote