#Need help getting correct explanation

51 messages · Page 1 of 1 (latest)

fathom haven
tired crescentBOT
fathom haven
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Would the limit be x->0?

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Because direct sub gave 0

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Or did i have to do something else to the equation to get an answer

vestal spear
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yo

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need help

fathom haven
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Yeah im not sure what i did wrong

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Did i have to do something to the equation? i just plugged pi cause i remember doing that on a past assignment and getting it right so i thought it was the same thing

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Or did i not explain enough

vestal spear
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yo

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got formula of x

fathom haven
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?

fleet bloom
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well, just because a function is defined at some value, doesn't mean the limit of that function exists at that value

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in this case it is true, but you have to prove it

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for instance if I let $f(x) =
\begin{cases}
1 & x = 0 \
\frac{1}{x} & x \neq 0
\end{cases}$, then $f(0) = 1$.

Then from that can I conclude that $\lim_{x \to 0} f(x)$ exists?

spare fableBOT
fathom haven
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Would i prove it by replacing (x+sinx) with (pi+sinPi)?

fleet bloom
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well okay, first thing I need to know is what is your definition of limits existing

fathom haven
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It can approach from left and right

fleet bloom
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so this is the core idea of limits: limits actually don't care about what happens at the limit, they only care what happens in the area around the limit

fleet bloom
fathom haven
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Im lost now

fleet bloom
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like how do you 🫵 prove that a limit exists

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I'm gathering that you haven't been taught epsilon delta

fathom haven
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No

fleet bloom
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so in your class, how have you been taught to prove that a limit exists

fathom haven
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our class is weird she post the notes in canvas to copy down before class and she hands us a worksheet to do

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I thought you can prove a limit exist if on a graph it approaches a point?

fleet bloom
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yeah sure, but do you have a rigouorous idea of what that actually means?

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it's fine if you don't

fathom haven
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Idont

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Thats why im a bit confused on all of this

fleet bloom
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because in that case the answer really would just be something like "the graph of sin(x+sin(x)) approaches a point at x=pi so the limit exists"

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but it's not really a satisfactory answer, lmao

fathom haven
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Would i need to prove it exist coming from left and right?

fleet bloom
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of course, but have you actually been taught how to do that?

fathom haven
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I dont think so

fleet bloom
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then, there isnt really a point in trying that... lol 🤷‍♂️

fleet bloom
analog prairie
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limit exist only if the left hand side and right hand side limit exist and are same

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if we use left hand side limit, replace x with pi-h

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and for right hand side, replace x with pi+h

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and check whether they both are same or not

fathom haven
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I watched some videos and I think I understand it a bit more now

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since it both comes out to 0 it means the limit exist right?

fathom haven
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Im not sure if i did it right

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Since i got -5 and 5 do limit doesnt exist right

analog prairie