Question

Find vertical asymptotes and prove with limits of f(x) = ((x^2+x)/(x^2-1))

Answer 1

\[f(x) = ((x^2+x)/(x^2-1)) \]

Answer 2

how do we define a vertical asymptote

Answer 3

as x approaches a number, y value gets closer to infinity or negative infinity

Answer 4

but why is it that only x=1 is a vertical asymptote and not x = -1

Answer 5

because when x= -1 , f(x) = 0/0, and we must use l'hopital rule to find lim of f(x) which gives us lim =1

Answer 6

how do i use that rule? can you please explain to me

Answer 7

when you have f(x) of the form of 0/0 or \(\dfrac{\infty}{\infty}\), then you can apply l'hopital rule to find the lim, just take derivative both numerator and denominator , and then take lim of it. If it is of those form, again, take derivative until you can take limit.

Answer 8

thank you

Answer 9

Do you actually mean "prove" with the \(\epsilon-\delta\) definition, or do you just need to compute?