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Christos
Group Title
Limits,
http://screencast.com/t/MeamUq9EgG8h
I heard there is a rule about "powers" when it comes to limits like this in order to solve them? Can you tell me the rule please?
 one year ago
 one year ago
Christos Group Title
Limits, http://screencast.com/t/MeamUq9EgG8h I heard there is a rule about "powers" when it comes to limits like this in order to solve them? Can you tell me the rule please?
 one year ago
 one year ago

This Question is Closed

UnkleRhaukus Group TitleBest ResponseYou've already chosen the best response.0
Is this your question ?\[\large\lim_{x\to+\infty}\frac{3x+1}{2x5}\]
 one year ago

zepdrix Group TitleBest ResponseYou've already chosen the best response.2
Yes there is a nice little shortcut, which is what you must be referring to. I'm trying to think of how to explain it. Since it's an infinite limit, we only need to worry about the `leading` term (highest power on top and bottom). Compare them, if they're equal degree, the limit will approach the ratio of their coefficients. In this case, 3/2.
 one year ago

UnkleRhaukus Group TitleBest ResponseYou've already chosen the best response.0
when \(x\to+\infty\), the ratio will ok like \(\frac{3x}{2x}\)
 one year ago

Christos Group TitleBest ResponseYou've already chosen the best response.1
you mean like 3/2 ??
 one year ago

Christos Group TitleBest ResponseYou've already chosen the best response.1
and when x>inf 3/2 ?
 one year ago

zepdrix Group TitleBest ResponseYou've already chosen the best response.2
Both x's are approaching negative infinity, so you can think of the negatives cancelling each other out, giving us the same 3/2 as with before :)
 one year ago

Christos Group TitleBest ResponseYou've already chosen the best response.1
What about higher power at the denominator or the numerator separately
 one year ago

Christos Group TitleBest ResponseYou've already chosen the best response.1
@zepdrix ?
 one year ago

zepdrix Group TitleBest ResponseYou've already chosen the best response.2
It might help if you see an example and just think about it logically. \[\large \lim_{x \rightarrow \infty}\frac{\color{green}{x^22x+3}}{\color{royalblue}{x7}}\] The green part represents a parabola, while the blue part a line. Which one will grow towards infinity faster? A straight line or a parabola?
 one year ago

zepdrix Group TitleBest ResponseYou've already chosen the best response.2
what? XD lol
 one year ago

Christos Group TitleBest ResponseYou've already chosen the best response.1
uhm I think its the whole numerator? I am not sure :D
 one year ago

zepdrix Group TitleBest ResponseYou've already chosen the best response.2
noooo it's not :O See how the `power` on x is larger in the top? We can't apply the same rule we used before, since the highest powers of x `do not match`.
 one year ago

zepdrix Group TitleBest ResponseYou've already chosen the best response.2
dw:1369665937413:dwWhich one of these functions is growing upwards faster? :O
 one year ago

zepdrix Group TitleBest ResponseYou've already chosen the best response.2
The curve or the straight line? :D
 one year ago

Christos Group TitleBest ResponseYou've already chosen the best response.1
numerator = denominator?
 one year ago

Christos Group TitleBest ResponseYou've already chosen the best response.1
Eeeh i mean that high one not the straight one the other one grows faster
 one year ago

zepdrix Group TitleBest ResponseYou've already chosen the best response.2
Yes good good, the curvy one grows faster.
 one year ago

zepdrix Group TitleBest ResponseYou've already chosen the best response.2
\[\large \lim_{x \rightarrow \infty}\frac{\color{green}{x^22x+3}}{\color{royalblue}{x7}}\]The `green` part is THAT type of function, the curvy one. So we can think of it this way, as the numerator and denominator approach infinity, the numerator is "winning", it's getting there faster. So the limit will approach infinity.
 one year ago

zepdrix Group TitleBest ResponseYou've already chosen the best response.2
That too confusing? :3 stick with the math rules?
 one year ago

Christos Group TitleBest ResponseYou've already chosen the best response.1
same applies for x>inf ? and what about the denominator having the highest power?
 one year ago

zepdrix Group TitleBest ResponseYou've already chosen the best response.2
Let's look at the reverse a moment. \[\large \lim_{x \rightarrow \infty}\frac{\color{royalblue}{x7}}{\color{green}{x^22x+3}}\] Now the BOTTOM is a larger degree than the top. So the bottom is "winning", approaching infinity faster. So our limit will approach \(\large \dfrac{1}{\infty}\) which is the same as saying, it's approaching zero. The denominator is getting bigger and bigger faster than the top, so the fraction becomes smaller and smaller.
 one year ago

zepdrix Group TitleBest ResponseYou've already chosen the best response.2
Negative infinity is a little trickier, since even powers will mess things up sometimes... I'm not sure how to explain that part properly :3
 one year ago

Christos Group TitleBest ResponseYou've already chosen the best response.1
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 one year ago

UnkleRhaukus Group TitleBest ResponseYou've already chosen the best response.0
Well done @Christos ! \(\LARGE\mathcal{CONGRATULATIONS!!}\)
 one year ago
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