Curve sketching | Mathematics | Page 1

distant orchid Sep 17, 2024, 3:09 PM

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karmic sinewBOT Sep 17, 2024, 3:09 PM

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upbeat snow Sep 17, 2024, 3:32 PM

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distant orchid

What have you tried?

distant orchid Sep 17, 2024, 3:33 PM

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Tried with long division, but it starts getting complicated

hollow kiteBOT Sep 17, 2024, 3:37 PM

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bacc

upbeat snow Sep 17, 2024, 3:44 PM

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We can approximate this limit using reasoning

distant orchid Sep 17, 2024, 3:44 PM

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hollow kite **bacc**

I wanna ask that how you come up with this?

upbeat snow Sep 17, 2024, 3:46 PM

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If g(x) is a skewed asymptote of f(x) then the limit should be 1 for large x as they get very very very close to each other

distant orchid Sep 17, 2024, 3:47 PM

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Yes

hollow kiteBOT Sep 17, 2024, 3:47 PM

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bacc

upbeat snow Sep 17, 2024, 3:48 PM

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You can see here what the dominant term will be for large x

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[ \frac{a^2}{\frac{ab}{2}} = 1 ]

hollow kiteBOT Sep 17, 2024, 3:49 PM

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bacc

upbeat snow Sep 17, 2024, 3:49 PM

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And you solve for one variable, another stays free

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You can test it with desmos

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@distant orchid

distant orchid Sep 17, 2024, 3:57 PM

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Sorry I am still confused

upbeat snow Sep 17, 2024, 3:58 PM

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Explain

distant orchid Sep 17, 2024, 3:58 PM

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hollow kite **bacc**

This

upbeat snow Sep 17, 2024, 4:02 PM

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distant orchid This

Yea I did a typo it's supposed to be a^2

hollow kiteBOT Sep 17, 2024, 4:03 PM

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bacc

distant orchid Sep 17, 2024, 4:09 PM

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Oh yes I got it

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Is it a=1 b=2?

upbeat snow Sep 17, 2024, 4:18 PM

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distant orchid Is it a=1 b=2?

How did you get these values?

distant orchid Sep 17, 2024, 4:19 PM

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Long division

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Whatt

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@upbeat snow

upbeat snow Sep 17, 2024, 4:24 PM

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distant orchid <@587715738484211754>

Can you show your work?

distant orchid Sep 17, 2024, 4:27 PM

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I divided (ax-3)^2 by a^2 - bx, and it matches the first term of the quotient is-ax/b, which matches the y=mx+c format

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Then is it a=4 b=8?

upbeat snow Sep 17, 2024, 4:30 PM

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that seems more like it

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https://www.desmos.com/calculator/tuag5aknkr

Desmos

Desmos | Graphing Calculator

distant orchid Sep 17, 2024, 4:34 PM

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Can you explain why a=4 & b=8?

upbeat snow Sep 17, 2024, 4:34 PM

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???

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I should explain your solution?

distant orchid Sep 17, 2024, 4:36 PM

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I got that by accident, see the part b)? I integrate it back to match the denominator, haha!

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But I want to know what is the original method, maybe next time they don’t provide any hints

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Sorry for your confusion.

upbeat snow Sep 17, 2024, 5:35 PM

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distant orchid Sorry for your confusion.

You should get a = 4 with polynomial division

upbeat snow Sep 17, 2024, 5:44 PM

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distant orchid Sorry for your confusion.

I just did polynomial division and used b = 2a

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I got a = 4 or a = -4, so just a = 4 because a > 0

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upbeat snow Sep 17, 2024, 5:45 PM

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distant orchid I got that by accident, see the part b)? I integrate it back to match the denomi...

Since you already tried it, I assumed you did a minor mistake somewhere along the lines

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So by that I can show you the solution

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and compare it to mine

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but you were right a = 4 and b = 8, smart of you to look at b)

#Curve sketching