find the horizontal and vertical asymptotes of the curve....?

Question

y = ( x^2 + 9 ) / ( 9x^2 - 35x - 4 )

x =______
x =______
y =______

y = ( 2e^x ) / ( e^x - 7 )

x = ____
y = ____

Answer 1

y = (x^2 + 9)/(9x^2 - 35x - 4) = (x^2 + 9)/[(9x + 1)(x - 4)]. The vertical asymptotes occur where the denominator vanishes, so at x = -1/9 and x = 4. To find horizontal asymptotes, find lim (x -> +inf)(f(x)) and lim (x -> -inf)(f(x)). Both these limits are 1/9

I hope you get the idea and can do the rest by yourself.