Calculus Infinite Limit | Mathematics | Page 1

carmine urchin Feb 9, 2023, 9:20 PM

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Can someone go through this with me?

pastel portalBOT Feb 9, 2023, 9:20 PM

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carmine urchin Feb 9, 2023, 9:21 PM

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carmine urchin Feb 9, 2023, 11:43 PM

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I'm confused on the rationalization

carmine urchin Feb 10, 2023, 12:30 AM

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My specific problem is that I don't know how this turns into this

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This is an example of a similar problem

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How does (x+sqrtx^2+1)(x-sqrtx^2+1) turns into 1

frail dew Feb 10, 2023, 12:51 AM

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yeah im confused

carmine urchin Feb 10, 2023, 12:53 AM

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I mean I know it does, I check it with mathway and verified it's true. But I need someone to help me work through this problem

sick anvil Feb 10, 2023, 12:59 AM

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carmine urchin My specific problem is that I don't know how this turns into this

its difference of squares

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the two terms in the top are (-a+b)(a+b) = -a^2 +b^2 = -x

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a is 8x and b is sqrt (64x^2 -x)

sick anvil Feb 10, 2023, 1:00 AM

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carmine urchin How does (x+sqrtx^2+1)(x-sqrtx^2+1) turns into *1*

same idea, difference of squares

carmine urchin Feb 10, 2023, 1:01 AM

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So how does it turn into x?

sick anvil Feb 10, 2023, 1:01 AM

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thats whats left over after stuff cancels

carmine urchin Feb 10, 2023, 1:01 AM

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Do I have to go through the whole distribution and factoring?

sick anvil Feb 10, 2023, 1:01 AM

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mTlY9EOoiRg5hlVaiaV42iqHBj7lvRj6LwWV1YlyJFihQpUqRIkSJFihQpUqRIkSJFihQpUqRIkSJFihQpfgnD3uObKgko2bSAAAAAElFTkSuQmCC.png

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its a frequently occuring identity

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you could FOIL it if you wanted but it would be unnecessary

carmine urchin Feb 10, 2023, 1:02 AM

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How can I determine that though?

sick anvil Feb 10, 2023, 1:03 AM

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you can foil it in the general case to prove it if you want

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it would take like 3 lines

carmine urchin Feb 10, 2023, 1:03 AM

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I put it through mathway and there were like 2 dozens steps

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Is there an easier way?

sick anvil Feb 10, 2023, 1:03 AM

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forget the machines

sick anvil Feb 10, 2023, 1:04 AM

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carmine urchin Is there an easier way?

by recognizing that its a^2 - b^2 and simplifying

carmine urchin Feb 10, 2023, 1:05 AM

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Okay, so like can you walk me through the math? I feel like I still don't know what to do exactly

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Sorry I'm asking alot

sick anvil Feb 10, 2023, 1:05 AM

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first if you have (a+b)(a-b)

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= a^2 -ab +ab -b^2 = a^2 - b^2

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so if youre multiplying two terms with the same stuff inside, except one is addition and the other is subtraction, you end up squaring both things

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so you have sqrt(64x^2 -x) and 8x

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you can see it has the same form as (a+b)(a-b)

carmine urchin Feb 10, 2023, 1:07 AM

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Okay

sick anvil Feb 10, 2023, 1:08 AM

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8x is what changes signs, so its going to be (sqrt(64x^2 - x))^2 - (8x)^2

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square and square root cancels so you get 64x^2 - x -64x^2 = -x

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its the same idea for the second one

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it helps if you do the simplication yourself on paper

carmine urchin Feb 10, 2023, 1:10 AM

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Alright, when I get home I'll see if I can practice it right

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Appreciate your help alot

carmine urchin Mar 9, 2023, 4:44 PM

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#Calculus Infinite Limit