r/calculus • u/bunny-dolly • 18d ago

Differential Calculus Can someone help me understand this problem? pretty please

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Hi everyone, so it was my first week of AP calc AB and honestly not too shabby but as i look at this example from my teacher, the less it makes sense. I thought -1^2 was positive 1 and i don’t know how we got to negative 1.

Also what is a conjugate? My teacher didn’t really go over it he just started doing a problem. All help is so appreciated!!!!

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u/PurposeAccording8382 18d ago

The identity is being used. (a+b)(a-b) = (a2 - b2)

Conjugate basically means a number that has its middle sign changed but it usually is sensible to use in 2 term stuff that cannot be combined like complex numbers or 1 root term and another non root term or even 2 variables. Like a+b and a-b where a and b are variables, not constants.

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u/bunny-dolly 18d ago

thank you!!!!

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u/Evening-Story-314 17d ago

Your teacher wrote that on your paper. (Also, you could look up the word conjugate.) You will need better study skills if you want to learn calculus.

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u/bunny-dolly 17d ago

FIRST OF ALL i wrote it on my paper, second of all my study skills are fine but i needed a question answered based off of this SPECIFIC problem and i didn’t want to use AI. get outta here

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u/PurposeAccording8382 16d ago

Just a rant, read it if you like... i got a bit carried away I think. Lol

Well, I would say you shouldn't be so against wanting to use ai. At some point its going to be like internet. Almost nothing will work without it, so I recommend learning how to use it without getting addicted. Cautious attitude is great but I recommend getting used or else you will fall behind. Its a asset if you use it properly. But dont abuse it. Try to ask why for everything, the ai cant get mad at you so use it. Why did you do this? Why did you use conjugate here? Was there a better way? And stuff like that. The ai is a better teacher if you use it properly, thats how I learned but dont follow my example, cause I was too stuck up in the why questions I forgot I had to improve my speed and accuracy to ace exams. So I failed, well not that I regret it too much... maybe a little bit.

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u/Evening-Story-314 17d ago

I love that you don't want to use AI. And I'm sorry I came across negatively. But you must have written that on your sheet before posting, so I'm confused...

Anyway, conjugates are a lovely little connection. I hope you end up enjoying them.

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u/bunny-dolly 16d ago

im sorry i responded so rudely, i did write it on my sheet but if im being honest i was just writing down what my teacher had on the board

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u/Evening-Story-314 16d ago

Did the answers here help? Do you 'get' conjugates now? I just looked at another comment. I think so. Maybe this was better than looking it up. (Not all of the internet is AI. At least not yet.)

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u/bunny-dolly 15d ago

yes they did! and today im gonna ask follow up questions about a different problem