calculus hard questions?

Question

1. Find the horizontal and vertical asymptotes of the curve.
y = (7 x + 6)/(x - 7)

i got 7 for x but whats y=

2. Find the horizontal and vertical asymptotes of the curve.
y = (x^2+2)/(7 x^2 - 34 x - 5)
x = (smaller value) is it 0
x = (larger value) is it 34?
y = no idead

3. Find the horizontal and vertical asymptotes of the curve.
y = (4 e^x)/(e^x - 5)
x= i got no idea how to solve for e
y= i got no idea what to do here

Answer 1

1. limit when x --> 7 is infinite then x = 7 is vertical asymptote

limit when x --> infinity is like (7x) / x = 7 then y = 7 is horizontal asymptote

2. 7x² - 34x - 5 = 0 for x = 5 and x = -1/7
limit in 5 or -1/7 is infinite then x = 5 and x = - 1/7 are two vertical asymptotes

limit in infinity is like x²/(7x²) = 1/7
then y = 1/7 is horizontal asymptote

3. e^x - 5 = 0 for e^x = 5 then for x = ln(5)

limit in ln(5) is infinite then x = ln(5) is vertical asymptote

limit in infinity is like 4e^x / e^x = 4 then y = 4 is horizontal asymptote