#How to solve asymptotes using limits
viral flintBOT
main fogBOT
Bennxy
undone elbow
Hello, you have to take the limit as x approaches ∞
In this case, the limit doesn't converge, so there are no horizontal asymptotes
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How to solve asymptotes using limits
frozen grove
An oblique asymptote is not a horizontal asymptote. To find an oblique asymptote, you need to write f(x) = mx+ b + g(x) where g(x) has a horizontal asymptote of y=0. Then y=mx+b is the oblique asymptote.
Fortunately, f(x) is already written that way for us, so you can just read off the oblique asymptote.
blazing dock
Ohh ok but when we used the limit for f(x) why didn't we divide 25x by x?
frozen grove
The 25x is separated by the plus sign.
blazing dock
So you mean this when we use limits to find the oblique asymptote?
$25x + \lim_{x \rightarrow \infty}20\cdot\frac{\left(\frac{50}{x^2+1}\right)}{x}$
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Bennxy
blazing dock
Do we only apply the limit at infinity for the fraction, and not to other terms?
undone elbow
Yes, and it approaches 0
coral dome
i think it applies to all terms
undone elbow
Yes, and it approaches 0
Follow what O Dog said. In this case, you have separated the linear term. The rest of the expression approaches 0, so the linear term is the oblique asymptote
If you had something like 25x + x², then there's no oblique asymptote because x² approaches inf
blazing dock
Aha ok
So do we apply the limit at infinity for 25x or not?
Because if we do we will get 25*inf
Or do we need to divide by x?
How does that work?
frozen grove
Really, you don't apply the limit at all.
frozen grove
An oblique asymptote is not a horizontal asymptote. To find an oblique asymptote...
Do this. If you really want to apply a limit, you should do it on the side to prove that g(x) goes to 0.
blazing dock
Ohh ok
I saw this a while ago and thought that we should use the limit over the whole function
Does anyone have any resources for this topic?
frozen grove
That image is the same as what I said. You can do that if you prefer.
blazing dock
Hahaha damn sorry man, that image looked more obvious with the functions and stuff
blazing dock
That image is the same as what I said. You can do that if you prefer.
Do you have any resources on this topic that I can learn from?
frozen grove
Khan academy: oblique asymptotes is my best guess.
blazing dock
Ok I'll check it out thanks
blazing dock
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