Checking my answers: Limits/graphing

[Spoon-]

Hey just checking if my I got these questions correct (I'm going to only put my final answer and post my solution if it's incorrect):

1. Lim (Srqt(x[sup:36mn5xui]2[/sup:36mn5xui] + x) -Srqt(x[sup:36mn5xui]2[/sup:36mn5xui] - x))
x->Infinity
= Infinity

2. Find Vertical and Horizontal Asymptotes:

y = x / (2x[sup:36mn5xui]2[/sup:36mn5xui] - 5x - 3)

V.A: x = -1/2, 3
H.A: y = 0

 

[stapel]

2. Find Vertical and Horizontal Asymptotes: y = x / (2x[sup:3mh72jc9]2[/sup:3mh72jc9] - 5x - 3)

V.A: x = -1/2, 3
H.A: y = 0

I get the same values.

1. Lim (Srqt(x[sup:3mh72jc9]2[/sup:3mh72jc9] + x) -Srqt(x[sup:3mh72jc9]2[/sup:3mh72jc9] - x))
x->Infinity
= Infinity

I get a different value. Please show your work and reasoning. Thank you!

Eliz.

 

[Spoon-]

Opps... I caught my mistake lol... I forgot about the denominator.
Okay, I'm stuck I can't get it after multiplying by conjugate.

Lim (Srqt(x2 + x) - Srqt(x2 - x))
x->infinty
= Lim 2x / ((Srqt(x2 + x) + Srqt(x2 - x)))
x->infinty

...then I don't know what to do :?

EDIT: I think I figured it out. Is it limit = 1?

 

[stapel]

EDIT: I think I figured it out. Is it limit = 1?

That's what I got. :wink:

Eliz.