precalculus

[proven void]

fine

[willow bear]

bruh

ok

so hes just cruel

[queen shoal]

is gamma function x! or something i think he told me about it

[willow bear]

aint NO FUCKING WAY hes gonna hand you a function whose DEFINITION involves IMPROPER INTEGRALS when you're looking for BASIC DERIVATIVE PRACTICE.

[queen shoal]

ok

[willow bear]

yes kind of

its derivative is not really easily expressible in terms of anything

[vapid plaza]

Your friend is trying to give you a hard time from what it looks like

Lol

[willow bear]

except another moderately nasty integral

[queen shoal]

ok then

[willow bear]

as neurotypicals typically tend to do, stemming from the belief that math is for nerds and torture is funny.

[vapid plaza]

And they’re not even doing it correctly by giving you the goofy ass equation

[proven void]

neuro-what?

[willow bear]

neurotypicals

antonym of neurodivergent

[queen shoal]

is this easier

idk chain rule for dividing

[vapid plaza]

I think you’re looking for quotient rule

[queen shoal]

ok

thanks

[willow bear]

this one's doable but very very unpleasant.

because of the x^x

[vapid plaza]

Why don’t you just come up with some random functions yourself and try

[willow bear]

i have a collection

roughly in increasing order of difficulty

[queen shoal]

thanks

[thin surge]

I know how to do it all except the last one

[willow bear]

so then you know both the chain rule and the product rule, yes?

[thin surge]

yes

[willow bear]

then what is the issue?

[thin surge]

I never did any math with "ARCTAN"

[willow bear]

$\tan^{-1}$ ?

[obsidian monolith]

|Ann⟩

[proven void]

what is the derivative of arctan(sqrt(x))?

I mean prolly the derivative of tan^-1(x)

[willow bear]

do you know what d/dx arctan(x) is

it might appear on your table

here we go again deleting all your msgs...

[proven void]

I know derivative of arctan(x) because of cookbook 1/x^2 + 1

but dunno how they got there tho

[willow bear]

missing parentheses, you meant 1/(x^2 + 1).

anyway you can derive it via the chain rule or implicit differentiation

or you could look up how to differentiate inverse functions generally

[viscid thistle]

hi, need help, sorry, and thanks.

in this problem
lim x-> -2

(x+2) (x³ - 10x² + 24x - 50)

x+2

i can cancel the denominator, how about the rest of numerator? should i keep factoring them or i can stop there?

[willow bear]

why are you apologizing for doing exactly what the server is for?

also, two things

1. you should write fractions with a slash -- this will require both the numerator and the denominator to be properly parenthesized: in your case, (x+2)(x^3 - 10x^2 + 24x - 50)/(x+2). if this is hard to do, it is better to write on paper.

2. after your cancellation, what you are left with is:

$\lim_{x \to -2} (x^3 - 10x^2 + 24x - 50)$

[obsidian monolith]

|Ann⟩

[willow bear]

remember that the whole reason you had to do any factoring and cancellation last step was because direct substitution led you to 0/0 (which is a sign you need to do something else)

but here you are left with a polynomial. a continuous function into which you can plug things without worry.

[viscid thistle]

so since it will not equal to 0/0, i don't need to use the rational zero theorem again even if i can? (in the video i watched, he did it twice so I'm not sure how to proceed)

[willow bear]

show the video and timestamp

before you do this:

when calculating limits like this, your motivation for doing anything is to make direct substitution possible.

the only thing that was stopping you was the division by zero.

but that isnt a thing now.

direct substitution works, therefore direct substitution is all that's needed -- and so doing anything else is extra work that is not required and not helpful.

[viscid thistle]

https://youtu.be/yx2RetjV1Bo?si=Z1fCyRKblqEsAlRc

5:43

(this is only for factoring 5 term polynomials, i watched it so i can factor mine)

[willow bear]

ok so that's about factorization, not about limits.

[viscid thistle]

thank you very much!!! thank you really!

[willow bear]

here it matters that you are calculating a limit.

[viscid thistle]

okay thank you again, just to confirm so I don't need to ask many times, as long as i managed to make the uh.. expression(?) that will not equal to 0/0, it's good?

[willow bear]

0/0 and infty/infty are the two most common indeterminate forms

there is also infty - infty sometimes

[potent oxide]

Guys give me good book for precalculus

[proven void]

maybe openstax calculus

there is also pre calculus version

[potent oxide]

Iam very good at pre

Am good at functions and sum

[proven void]

I only used the calculus one, so I cant really say anything about the pre

[potent oxide]

Just need good book for it

[proven void]

maybe #book-recommendations '

[potent oxide]

I gonna try openstax

[viscid thistle]

hello me again. is this the correct way to write fraction with variable?

[proven void]

you are asking if you did the polynomial division correctly

[viscid thistle]

oh sorry no, the way i write the fraction with variable, not sure if that's where you put the x

like -23/3 x²

i just need to know where the placement of x in the fraction

thank you

[proven void]

numerator

[queen shoal]

how do i do this

[austere girder]

can I get help with a calc one question?
idk if this is the right channel

[queen shoal]

send it

[austere girder]

its about the fundamental theory of calculus

i mainly guessed with these questions but i want to understand how you get them

[queen shoal]

oh idk i only know how to find derivatives of functions

[austere girder]

yeah im almost at the end of the chapter

where should i go for calc help?

[queen shoal]

you can go to #❓how-to-get-help or just leave it here

[proven void]

that you expand and simplify by taking the x^20 out I think

[willow bear]

expanding (2x - x^4)^14 will give you a bunch of terms which are powers of x

you're asked to find and return the term where the exponent on x is 20

[golden cairn]

Sorry I already solved it I should have deleted it

I forgot

[desert void]

try #calculus

[willow bear]

@old bane so your problem is to find the range of $f(x) = \frac{|x-4|}{x-4}$, yes?

[obsidian monolith]

|Ann⟩

[old bane]

yes

[willow bear]

ok, progress so far?

[old bane]

Im not able to understand this question

[willow bear]

which part of the question confuses you?

or did you mean that you can't understand my question of "how much progress do you have so far?"

[old bane]

like how do I solve it

I don't know from where to begin

[willow bear]

ok, so let's start with a more general question

do you know what |these| bars represent?

[old bane]

mod

[willow bear]

ok, can you tell me the definition?

like |x| = ...

[old bane]

eg I-5I=I5I

they turn any no +

[willow bear]

1. do not use the capital letter I as a substitute for the vertical bar |.
2. that's an example and not a proper definition.

[old bane]

my bad

[willow bear]

again not a full proper definition.

$|x| = \begin{cases} x & x \geq 0 \ -x & x < 0 \end{cases}$

[obsidian monolith]

|Ann⟩

[willow bear]

does this look familiar to you?

[old bane]

yes

[willow bear]

ok

now tell me

what happens when you calculate |x|/x ?

[old bane]

1?

[willow bear]

always?

[old bane]

uhm ig yes

[willow bear]

you guess?

[old bane]

always 1

[willow bear]

what if x = -10? what will |x|/x be then?

[old bane]

1 only

[willow bear]

are you 120% sure

[old bane]

yes

[willow bear]

ok what's |-10|?

[old bane]

|10|

[willow bear]

|10| is?

[old bane]

|10| only

[willow bear]

you claim that it isn't equal to 10 itself?

[old bane]

it is

[willow bear]

then why did you just say "|10| is equal to |10| only, and not to anything else ever"

[old bane]

ok |10|=10

[willow bear]

right

so |-10| = 10 as well.

now, 10/(-10) is?

[old bane]

yes

-1

[willow bear]

ok

so you see that |x|/x is not equal to 1 always, yes?

[old bane]

oh

yes

[willow bear]

so if you refer again to this definition:

$|x| = \begin{cases} x & x \geq 0 \ -x & x < 0 \end{cases}$

[obsidian monolith]

|Ann⟩

[willow bear]

(which you could've looked at the first time around, but for some reason you didn't)

you will notice that |x|/x equals 1 for positive x, and -1 for negative x, and that it never returns any other values.

[vapid plaza]

What is the range of |x-2|?

[old bane]

idk

ve+?

[vapid plaza]

Yes

(But isn’t it called +ve usually?)

[old bane]

mb bro

[vapid plaza]

Well actually

The answer is [0, +infinity) (so it can be zero as well as positive)

Because when x+2=0, the absolute value of it is also zero

[old bane]

can u explain

[vapid plaza]

When x=-2, we have x+2=0, so |x+2|=0

[old bane]

ok then

[vapid plaza]

And actually you can get any nonnegative number c by setting x=-2+c, so that x+2=c and so |x+2|=c too

On the other hand, it is impossible for absolute value to be negative

[old bane]

c= complex no?

[vapid plaza]

So the range of |x+2| is [0, +infinity)

what

No

Bro I said c is some nonnegative number

[old bane]

ok but the ans in my book is (-infinity,0]

[vapid plaza]

Well we are not done with the problem yet

[old bane]

ok go ahead

[vapid plaza]

You want to find the range of 1 - |x+2|

[old bane]

yes

[vapid plaza]

so try to think of 1 - something in [0, +infinity)

Then the largest number we can end up with is 1-0=1

and any smaller than that we can get

But larger than 1 we cannot get

[old bane]

@vapid plaza

[vapid plaza]

Idk how to explain it simpler

[proven void]

(-infinity, 1]? wdym (-infinity. 0]?

,w range of 1 - |x-2|

[obsidian monolith]

Results provided by WolframAlpha

Click here to refine your query online
Upgrade to WolframAlpha Pro!

Requested by xbz24

[proven void]

if you check f(2) = 1 so why 0?

the maximum value you can get out of

1 - | x - 2|

is when | x -2 | = 0

which is when x = 2

1 - 0 = 1?

the range is (-infty, 1] clearly

[proven void]

take a screenshot

[willow bear]

that's not what "take a screenshot" means

[proven void]

${x \in \mathbb{R} \mid \frac{1}{x} < \frac{4}{x}}$

[obsidian monolith]

milanesa de pollo

[proven void]

how do I represent this set as interval notation?

sorry for the bad latex

[willow bear]

the latex is much better than what's typically seen as "bad" here

but anyway you are asking how to solve the inequality 1/x < 4/x, yes?

[proven void]

yeah, sorry.

[willow bear]

do you know how to solve inequalities in general?

[proven void]

I think I can move the 4/x to the left side and I am finished I think

xdd

sorry

[willow bear]

move [...] to the left side
bad

what exactly are you planning to do?

add something to both sides? multiply by something on both sides? be precise. it matters.

[proven void]

just substracting both sides

[willow bear]

ok, so you subtract 4/x from both sides.

what do you get from that?

[proven void]

I think its easier to subtract 1/x

I get $ 0 < \frac{3}{x}$

[willow bear]

"I think its easier to dodge the question instead of answering it directly"

but ok yeah

you get 3/x > 0

so what set does x live in

[proven void]

reals but not zero

[willow bear]

are you sure?

(i will ask you this regardless of if your answer is right or not)

[proven void]

aaaaaaaaaaaaaaaaaaaaaaaaaaa

no sorry

(0, +infty)

if we plug a negative sign automatically its false

[willow bear]

yes

3/x > 0 <=> x > 0

[proven void]

,, \set{x \in \mathbb{R}}{|x| > 3}

[obsidian monolith]

milanesa de pollo

[proven void]

may I ask about this one

[willow bear]

what about it

wait

#precalculus message

i helped you with THIS EXACT PROBLEM a week ago.

so reread that convo @proven void

[queen shoal]

can someone help me fiind the derivative of 6^x

i currently have 6^x * (x/6+ln(6))

[willow bear]

show work?

that's incorrect.

[queen shoal]

but apparantly it is 6^x * ln(6)

ok

[willow bear]

but i have a feeling that i know where you screwed up.

(still, i'll need to see your work to point it out)

[queen shoal]

i can rewrite 6^x to e^log(6)x

log is natural log

[willow bear]

well i had in fact premoved ``$e^{\ln(6)\cdot x}$ and chain rule.'' in this convo.

[obsidian monolith]

|Ann⟩

[willow bear]

ok, so what did you do next? do you have your work on paper so you can take a picture?

[queen shoal]

its messy

and has work from another problem

[winter comet]

try showing and then try to explain if need be

[queen shoal]

ill just type it

ok

[winter comet]

or that

either way

[willow bear]

ok alright

[queen shoal]

I did it again

[willow bear]

the derivative of log(6) is not 1/6.

[queen shoal]

oh

[willow bear]

also miswritten product rule.

[queen shoal]

isnt the derivative of log(x) 1/x

[willow bear]

yes d/dx log(x) = 1/x.

but log(6) is a constant.

[queen shoal]

so is it 0?

[willow bear]

yes it's 0.

also (fg)' is not equal to (f * g') times (f' * g).

review product rule.

[queen shoal]

is it (f * g') + (f' * g)

[winter comet]

yes

[queen shoal]

oh ok

[winter comet]

btw by log do you mean natural log

[queen shoal]

yes

[winter comet]

ok

[queen shoal]

thanks

i understand now

[willow bear]

log(6)*x is just a linear function

[queen shoal]

ok

[winter comet]

you COULD also know the rule d/dx(a^x) = a^x * ln(a) where a is a constant

but of course its good to know how they got there, and also you need to know how to do it when it isn't a constant so yeh

[queen shoal]

ok

i have (6^x)+(x^x)/2^x

i used quotient rule but wolfram it changed x^x/2^x into x^x * 2^-x

[willow bear]

$6^x + \frac{x^x}{2^x}$?

[obsidian monolith]

|Ann⟩

[queen shoal]

yes

[willow bear]

ok

[willow bear]

yeah, so?

[queen shoal]

then used product rule

is that what i should be doing?

[willow bear]

yeah, so?

[queen shoal]

instead of using quotient rule

[willow bear]

does every problem have exactly 1 and only 1 legal solution path?

[queen shoal]

no

but is it easier to do that

[winter comet]

using the product rule instead of the quotient rule is good a lot of the time, but sometimes its just simpler to use the quotient rule

honestly up to u

[willow bear]

if you wanted to ask whether there was a better method than what you did, then you should have asked that lol

but yes generally quotient rule is hairy

[queen shoal]

oh ok

[queen shoal]

ok

[willow bear]

if you can avoid using it, it's probably a good idea to do so

[queen shoal]

ok

[proven void]

after visualizing it on the real line it made more sense

may I ask about |x + 2 | < 3 tho?

is it (-5,1)?

[willow bear]

i don't know, is it?

how did you get (-5, 1)?

do you have the number line you drew for it?

[proven void]

at this point im just guessing not sure what to do

[willow bear]

do you remember how to view absolute value as distance? Y/N

[proven void]

n

[spice breach]

does anyone know well about the simpson's paradox?

[proven void]

distance to 0?

[willow bear]

#probability-statistics is a better place to ask this -- and be more concrete.

[spice breach]

ty

[willow bear]

|x| is the distance from x to 0 yes.

but here you've got |x+2|, which is the distance from x to what point?

[proven void]

0

?

[willow bear]

|x+2| is not the distance from x to 0.

[proven void]

to

-2

[willow bear]

are you sure?

[proven void]

no im just guessing

[willow bear]

(i would have asked this regardless of if you're right)

[spice breach]

|x+2| is the distance from 0, no?

[willow bear]

distance is never just "from something", distance is between two things.

anyway

@proven void |a - b| is the distance between a and b.

this is true always.

do you know and understand this?

[proven void]

no

[willow bear]

ok, would you like to go through it to understand it?

yes/no

[proven void]

since when is that true

[proven void]

y

[willow bear]

since 1806, when the concept of absolute value was introduced.

[willow bear]

ok.
so first, WITHOUT REFERRING TO THE CONCEPT OF ABSOLUTE VALUE,
can you tell me, in words, how you would find the distance between two points on the number line?

[proven void]

the largest - the smollest

is the distance

[willow bear]

ok

so let's say the points are called a and b

if a > b, then what would the distance be?

[proven void]

a-b

[willow bear]

and if a < b instead?

[proven void]

b-a

[willow bear]

right.

so if a > b [i.e. if a-b > 0] then dist(a,b) = a - b
and if a < b [i.e. if a-b < 0] then dist(a,b) = b - a = -(a-b)

do you agree or disagree?

[indigo dew]

agree

[proven void]

agrred

[willow bear]

the question was not addressed to you.

[willow bear]

ok cool

do you now understand why |a-b| is the distance from a to b?

y/n

[indigo dew]

yes

[proven void]

yeah

[willow bear]

again the question was not addressed to you.

[indigo dew]

ok bye gn im going to study chem

[willow bear]

ok @proven void now we've gone over this,

can you justify why |x+2| is the distance from x to -2?

[proven void]

yeah

but

what now?

[willow bear]

well

[proven void]

how to draw it on the real line

[willow bear]

now look at the original equation

|x + 2| < 3

we can rewrite it in words:

the distance from x to -2 is less than 3.

do you understand the translation? Y/N

[proven void]

distance between x and -2 is less than 3

yeahh

[willow bear]

ok.

[proven void]

what about it

[willow bear]

well.

do you understand how to draw that sentence on the number line?

Y/N

[proven void]

I dont get it

its the original drawing

[willow bear]

what exactly do you not get?

[proven void]

,rotate

[proven void]

both non inclusive

is that good?

🤔

[willow bear]

is this another guess? or are you now able to say for certain that you drew "x is closer than 3 units to the point -2" correctly?

[proven void]

I think I understand it a little better no0w

[willow bear]

do you mean math in general

or do you mean this thing we just went thru in detail

no, you won't get away with deletion

you said "math is confusing".

[proven void]

im not guessing

now I understand it better

[proven void]

but I deleted

because i wasnt being clear

[spice breach]

@proven void try drawing this
|x-2|>4

[queen shoal]

Found the derivative of some random function on my shirt (replace y with x)

[spice breach]

try doing with y

[spice breach]

yes good I think you know these problems well now

if you want to challenge your self you could try doing questions with
x^2

this will probably come in your next unit

or you could try doing a mix of 2 different inequalities

and finding a value of x that complements both the inequalities

[proven void]

I literally suck at math

[spice breach]

how old u?

[proven void]

I will try to find those exercises

[queen shoal]

Ok

[candid mortar]

so is the derivative function kind of like a conversion rate? like if we find an infinitesimally small change in y over x, is that the value that we can multiply by any input from the domain to find the instantaneous rate of change at that point of x?

for example, if i had x^2, if i find an infinitesimally small change in y over x, is the answer 2? since the derivative is 2x?

[summer ruin]

no

the derivative is the rate of change of the function at the point

[empty willow]

hi guys

how to start pre calc

like for beginners

🙂

[candid mortar]

dang. It makes sense to me how we find it at a singular point, but i cant get an intuition for the function that can find it for any given point

[summer ruin]

what

[candid mortar]

this sort of makes sense to me to find the rate of change for 1 value of x, but i dont understand how a function can find the instantaneous rate of change at any given point

[summer ruin]

plug in every single point in the definition

[willow skiff]

Notice that doing the right hand side gives you another function also

It helps if you look up some simple examples

Like y = x^2

[candid mortar]

will do, thank you

[willow skiff]

No worries

So like knowing that the right hand side is also a function, that explains why you can plug in any value of x
To find the derivative (the gradient of the tangent line) at that point

[proven void]

is this upper bounded?

if so by what? 2?

why is math so hard tho

yeah its upper bounded

by 2 and 1

I just realized

what about lower bounds?

there isnt?

[random yoke]

0

-1

etc.

[proven void]

true that

thanks

[proven void]

how do I get infimum and supremum of this?

,, \set{\frac{1}{n}}{n \in \mathbb{N}}

[obsidian monolith]

milanesa de pollo

[proven void]

how do I get infimum and supremum?

[summer ruin]

try to find a number A such that A >= 1/n for any natural n

then reduce that number as much as possible

[proven void]

its not possible then you are saying

[summer ruin]

it is possible

[proven void]

its 1

no idea, im just guessing at this point

that would be the infimum?

[summer ruin]

well is there a smaller number than 1, such that it's also bigger 1/n for any natural n?

no

[proven void]

what are we looking for?

infimum or supremum?

im confused

[summer ruin]

supremum

[proven void]

supremum is 1

[summer ruin]

what do you think infimum is

[proven void]

not possible

[summer ruin]

why not

[proven void]

infimum is defined as greatest lower bound

I recognized there are some lower bounds for this function 0 , -1 , -2, -3, -4

[summer ruin]

by definition it also doesn't have to be part of the set

[summer ruin]

so is -1/2, -pi, -e^pi

infimum is the largest lower bound

[proven void]

thanks

waaait

so sup is 1 inf is 0?

i might have misunderstood something

[summer ruin]

yes

[proven void]

gotchu

i see i see

[proven void]

I wanted to ask

,, B = \set{\frac{n}{n+1}}{n \in \mathbb{N}}

[obsidian monolith]

milanesa de pollo

[proven void]

lower bounds: 1/2, 0, -1, . . .

upper bounds: 1, 2, . . .

interval notation: [1/2; 1[

infimum: dne

supremum: 1

?

[proven void]

wait, if supremum does not exist then immediately I can say sup and inf dne

[real crypt]

If this is precalc I'm dead

[remote sable]

How do I solve part a)? This is what I know for now

I would differentiate the equation of the curve to get gradient of the curve then equate it to 0. I would then sub in 4 which is the x coordinate of point p. This gives me the gradient. After this point do we sub into the equation of circle or what?

[jagged garnet]

Find the answer:

$$\lim{x=4}(7x/frac{5}{x-x^.5}$$

[obsidian monolith]

wind from the landscape

[winter comet]

eh

it looks bad when u dont know what it means

just see weird symbols and ur like nuuuuuuuuuuu

xD

[shadow summit]

$\lim_{x\rightarrow4}(7x\frac{5}{x-\sqrt{x}})$

[obsidian monolith]

TheLord26

[jagged garnet]

The exponent is .5 not 5

[shadow summit]

$\lim_{x\rightarrow4}(7x\frac{5}{x-\sqrt{x}})$

[obsidian monolith]

TheLord26

[jagged garnet]

7x=28

4-2=2

5÷2=2.5

5/2.5=2

28×2=56

Therefore the limit is 56

[proven void]

how do I find interval notation for this set?

I am trying to find the upper bounds

[winter comet]

why would there be bounds?

hold up what is the question asking

not the spanish i mean the notation

for y including all real numbers, y = x^2 - 3x + 2, for x including all real numbers...?

or wut

[proven void]

y is a real number x is a real number

[winter comet]

there wouldn't be any upper bound

its a parabola

goes up infinitely

right

[proven void]

i’m not sure tbh

i know it goes up infinitely

but dunno what that means in terms of upper bound

[winter comet]

are you writing the interval notation for the domain or the range, or both seperately, or both together

because idk how to do it both together

not sure if its a thing

[winter comet]

if you're talking about upper bound for the range

it goes up to infinity

if you're talking about upper bound for domain

it still goes to the right infinitely

right

cuz its a parabola

[proven void]

what about finding infimum and supremum for this shit?

[proven void]

im not sure but I think in this case its about the y axis

meaning infimum: greatest lower bound is f(3/2) = -1/4
sup: smallest upper bound: +inf

no idea really

I think I was talking about the range yeah

[winter comet]

ah

[proven void]

how can I write the rational number

0.122424. . .

as a fraction?

[winter comet]

1. how did you find it
2. how does it repeat

[proven void]

how did I find it?

in my homework problems? xD

how does it repeat?

0.122424242424242424242424

[winter comet]

was it like the result of a weird number?

[proven void]

no

look

one sec

[winter comet]

oh dang hmm

[proven void]

write the rational number 0.122424. . . as a fraction

its the translated exercise 11

[winter comet]

0.12424... and i have no idea ig lol

[viscid thistle]

It is 0.1 + 0.0242424….

[proven void]

seems easy but is tough

yes

[winter comet]

and whats 0.024242424...

[viscid thistle]

Calculate it yourself

Hint: what’s 24/99

[proven void]

how to express it as a fraction

mmm

,w 24/99

[winter comet]

💀

[obsidian monolith]

Results provided by WolframAlpha

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Upgrade to WolframAlpha Pro!

Requested by xbz24

[winter comet]

i forgot abt that lol

[proven void]

,w 24/990

[viscid thistle]

Bruh

[viscid thistle]

(24/99)/10

[obsidian monolith]

Results provided by WolframAlpha

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Upgrade to WolframAlpha Pro!

Requested by xbz24

[proven void]

thanks

[viscid thistle]

finally

[proven void]

how does that shit work though

like the 99 denominator trick?

[winter comet]

i haven't done the weird dividing by 9 stuff in a long time lol

[proven void]

123/990 is the fraction as a whole, I think

thanks

,w 123/990

[obsidian monolith]

Results provided by WolframAlpha

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Upgrade to WolframAlpha Pro!

Requested by xbz24

[proven void]

nice ^^

[normal ridge]

excuse me

but

can someone please explain limits

like what is c, delta, epsilon, and l

[proven void]

How do I check if this series is convergent or divergent?

,, 1,2,3,4,…

[obsidian monolith]

milanesa de pollo

[winter comet]

i mean

if you add whole numbers forever ur gonna get infinity

so its divergent

[proven void]

Nice

Thx

What about this series?

,, -1, -\frac{1}{2}, -\frac{1}{3}, -\frac{1}{4}, …

[obsidian monolith]

milanesa de pollo

[proven void]

Divergent, no?

[winter comet]

how do you figure?

[proven void]

If you add up all the numbers

You get $-\infty$

[obsidian monolith]

milanesa de pollo

[winter comet]

not necesarily

the fractions are getting smaller

also this is a sequence but details lol

but um

lets just say ur going to a wall which is 1 meter. first you go half the distance, so 1-1/2, then you go half of the remaining distance, so 1-1/2-1/4, then you go half of that remaining distance, 1-1/2-1/4-1/8... ect.

eventually you're going to get there

like eventually ur gonna get to 0

so that series converges

i'm pretty sure

[proven void]

Yeah

[winter comet]

not sure about this one though

i haven't had much practice with series, but i should knowing its in calc 2 😅

wait i think sequences are just a list, whereas series is where you add them
i think a converging/diverging sequence would be if you add all the terms and its either converging or diverging right

that was unclear

i said that unclearly

wait

[winter comet]

u might be right actually

i'm honestly not sure ☠️

[proven void]

,w -1/10000

[obsidian monolith]

Results provided by WolframAlpha

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Upgrade to WolframAlpha Pro!

Requested by xbz24

[proven void]

Its converging

[viscid thistle]

This is a sequence not a series

[proven void]

Sorry

[viscid thistle]

This is also a sequence

[proven void]

Yeah

Mb

[proven void]

Sorry

Is it convergent sequence

[viscid thistle]

You can find the general formula for the nth term and take the limit as n approach infinity

[proven void]

One sec

No idea

[winter comet]

oh thats the limit comparison test for series right?

or sequences

is that right

i've heard of the term and im guessing thats what it is

[viscid thistle]

That’s a different thing

[proven void]

Maybe $\lim_{n \to \infty} \frac{-1}{n}$?

[viscid thistle]

This is just a way to see if the sequence diverges or converges for large n

[viscid thistle]

Close, small typo

[proven void]

Im just guessing at this point

[winter comet]

yeah i mean you can plug in the first few terms

and see

its the summation from n to infinity of dat

but you dont take the summation when doing the limit

[winter comet]

mk

[proven void]

Ohhh

[winter comet]

rip

[proven void]

I seeeeeeeeee

[winter comet]

yeeeeeeeeeeeeeee

xD

[obsidian monolith]

milanesa de pollo

[winter comet]

that looks better ya

sum aint right

[proven void]

?

[viscid thistle]

You can see that this converges to 0

[winter comet]

this definitely does not converge to 0

[winter comet]

yeah but the og doesnt

its negative all the way thru

like -1 and then subtracting after that

[viscid thistle]

It does?

-1/(really large number) is just 0

But if it’s a series then it diverges

[winter comet]

no but look at the og series

-1 - 1/2 - 1/3 is not approaching 0

[viscid thistle]

Yeah duh

[winter comet]

right

[viscid thistle]

It approaches infinity

[winter comet]

so it doesnt converge to 0?

[viscid thistle]

It doesn’t

[proven void]

?

[winter comet]

so whats this then?

[viscid thistle]

The harmonic series diverges so why do you think this series converges

[viscid thistle]

That’s the limit for the nth term of the sequence as n approaches inf

[winter comet]

oh

and i was doing series

and you cant do that

i see

wait

maybe i see

hold on XD

[proven void]

,w Sum[-1/n, {n, 1, 1000}]

[obsidian monolith]

Results provided by WolframAlpha

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Upgrade to WolframAlpha Pro!

Requested by xbz24

[proven void]

so it diverges because it goes to -infinity

[viscid thistle]

Duh

This also goes in #calculus kinda

[proven void]

sorry

[viscid thistle]

Because limits

[potent oxide]

Dayum

[near sentinel]

Guys they finally taught us lhopital 🔥💯🔥

[willow skiff]

Students love LH but always forget to check if it's in the right form

0/0 or infinity/infinity

[near sentinel]

Yeahh, that's the reason our teacher wasnt teaching it to us, he said first do everything by lhopital so you can see the other stuff before it and not use the wrong stuff

[proven void]

I will be taught sequences today. next week limits

[willow bear]

do what it says

calculate f(1.1), calculate f(1), then calculate that fraction there

the instructions are fairly straightforward

your arithmetic is correct

but you might wanna tidy that up a little

i think you were able to do this on your own. what was blocking you? were you just overthinking?

[shadow summit]

Probably just wanted confirmation, not everyone is confident in their abilities/want to make sure they are on the right track.

Have you tried graphing the function?

[old bane]

no and idk how to

[proven void]

the radicals can’t have negative inside otherwise it’s imaginary

[shadow summit]

That will probably give you a deeper understanding of the question.

[shadow summit]

Use desmos.com

As you can see here the function doesn’t go past x=4 (nor is it defined at that point) and it goes to infinity when x=1 (think of 1/0)

[willow bear]

this can and should be said explicitly

[shadow summit]

Not a big deal though.

[willow bear]

big difference between that and "idk wtf the problem is saying" / "the problem stmt completely paralyzes me bc i have a debilitating phobia of all things math"

[shadow summit]

Well you can always try to help people nonetheless.

And if you can’t be bothered, then just ignore it.

[proven void]

how do I calculate this limit?

$\lim_{n \to \infty} (-1)^n \cdot n$

[obsidian monolith]

milanesa de pollo

[proven void]

can I use lhopi

also I got this limit by taking the general term in this sequence

-1,2,-3,4,…

I dont want to make it a xy problem

[willow bear]

a million times no!!!

anyway as you can see the sequence keeps going back and forth and further and further each time.

it doesn't approach anything.

[proven void]

oh, my bad

divergent then

[willow bear]

you can only even consider l'hopital when you are looking at the limit of a function defined on at least an interval or some other unbroken stretch of the number line.

not when it's only defined at integer points!!

[proven void]

how can I convert this to a general term a_n? 0, 1/2, 0, 1/3, 0, 1/4 so I can find limit?

[small gyro]

hello! I am trying to do this exercise for partial fractions and I can't find a way to get the right answer. I make it a system of equations where I find that A = B (which is true), and then when I try to substitute A into B for the rest of the equations, I consistently get incorrect numbers for C and A. (-31 and 25 respectively). Why is it that the method I'm using doesn't work, and how do I actually get the correct values for A B and C? (the answers being 1, 1, and -1)

[uncut mulch]

show your attempt

[small gyro]

oh lord, ill write it in chat. My working got quite messy because I started going insane over it

oops

i figured it out

for B(x+1)(4-x) I made a tiny flip of the sign where i wrote -3x instead of +3x

The lies always hide within half truths 😭

[vagrant nymph]

What did I do wrong ans is suppose to be 39.3

[empty willow]

malevolent shrine would be the correct answer

.

[winter comet]

is the entire page the problem?

[vagrant nymph]

The soln yes

I tried

I don't know what I did wrong

[winter comet]

this is calc 😂 bu ok lemme see

[vagrant nymph]

There is difference between them?

[winter comet]

yea precalc is like the stuff to learn like the basics for understanding calc and above

[vagrant nymph]

Bro calc is a chapter for us for next year they are teaching this for physics basic

So like I thought this is pre calc

[winter comet]

aha

[vagrant nymph]

Did u spot the mistake?

[winter comet]

ye

its uh

distributed wrong

or like the opposite of distributed wrong

it should've been

[vagrant nymph]

Oh ok

[winter comet]

yea

[vagrant nymph]

It's 3/10

[winter comet]

-3/10 ye

[vagrant nymph]

Yea forgot to type that

[winter comet]

wait sum still aint ri

hold onXD

[vagrant nymph]

Wait it's 3by 10

Only na

[winter comet]

oh right of course yah

yeah so its positive 3/10

now it shud be right

XD

[vagrant nymph]

Ty for help

[proven void]

how to find limit of $c_n = \frac{3n^2 + 2}{2n^3 + 5n}$

[obsidian monolith]

milanesa de pollo

[summer ruin]

it's the same as finding the limit of b_n

[proven void]

no

$2n^3 \neq 2n^2$

[obsidian monolith]

milanesa de pollo

[summer ruin]

that's not what I said and not what you asked

you asked how to find the limit of c_n, I'm saying the process is exactly the same as finding the limit of b_n

[proven void]

mmm

how to do that

[summer ruin]

how did you find the limit of b_n

[proven void]

is it 0?

[winter comet]

how did u get 0

[proven void]

,rotate

[summer ruin]

then do the same thing

[proven void]

,rotate

[proven void]

?

[winter comet]

yes

thats correct

[proven void]

got it thanks

here the limit doesnt exist

no?

same with this one, doesn’t exist

[summer ruin]

you need to argue why in both cases

[proven void]

how

[summer ruin]

why would you even try to guess it if you didn't even try to arrive at the answer?

try every limit solving technique you've learned so far

[proven void]

,rotate

[proven void]

there are no more techniques

there is nothing to do for D

[summer ruin]

try dividing by n^2

[proven void]

instead of n^3?

one sec

,rotate

[proven void]

how do I get rid of -4n

[summer ruin]

you don't need to

[proven void]

?

but the sequence is divergent

[summer ruin]

observe what you get here

[summer ruin]

can you explain why

[proven void]

its unbounded or something? like the 4n is infinity

everything will become infinity?

[willow bear]

-4n goes to -∞

so what does the numerator as a whole approach?

[proven void]

sorry

-inf

[willow bear]

yes

and the denominator?

[proven void]

5

the limit exist if the sequence is divergent?

?

[summer ruin]

nobody says that

you just didn't provide any explanation to why you believe the answer was that what you guessed initially

[proven void]

,rotate

[proven void]

is this enough proof E doesnt exist aswell?

it doesn’t converge

what would the limit be equal to? +inf?

or just is undefined

[summer ruin]

n^(3/2) is not equal to n^2 * n^(3/4)

[proven void]

oops

[half pollen]

How many 3-digit natural numbers $n$ are there such that the ones and tens digits of $n^2$ are the same as those of $n$?

[proven void]

-1/2

[obsidian monolith]

nyxie9151

[half pollen]

i think i'm very close lol 😭 can someone help me "finish the thought"

100 | n^2 - n

what's next?

actually i havee this

i don't understand what happens after ->

[proven void]

converges to zero?

[summer ruin]

yes

[proven void]

ty

[half pollen]

bruh

is this chatgpt 😭

[proven void]

how to compute $\lim_{n \to \infty} n(\sqrt{n+2} - \sqrt{n})$

[obsidian monolith]

milanesa de pollo

[proven void]

this is the tricky part, how to proceed?

[surreal crescent]

Why is it that integrals require dx, and how do you find the delta of one value?

[summer ruin]

same as before

factoring

[proven void]

but

is there any relevant root property here?

[summer ruin]

sqrt(ab) = sqrt(a) * sqrt(b)

[proven void]

im talking about sqrt(n+2)

mmm

what about that one?

[summer ruin]

you already learned in multiple previous exercises how to factor out an n out of the root

[proven void]

I can take a n^2 out of a root

but

[summer ruin]

n+2 = n*(1+2/n)

[proven void]

after the simplification I got this?

but this is still a divergent series

2/+inf

the final simplification is $\frac{2}{\sqrt{n+2} + \sqrt{n}}$

[obsidian monolith]

milanesa de pollo

[proven void]

still divergent

limit doesnt exist i guess

[summer ruin]

that's not what it simplifies to

there's n in the numerator, not n^2

[proven void]

but

here is n^2

[summer ruin]

it cancels out with another n down to n

and n^2 / n^(3/2) is not 1/sqrt(n)

[proven void]

wait

I did it a little better now

but its simplifying to

,, \frac{2 \sqrt{n}}{\sqrt{1 + \frac{2}{n}} + 1}

[obsidian monolith]

milanesa de pollo

[proven void]

dunno why math is that hard

but should be diverging

the sequence i mean

whatever

this exercise is fucked

[proven void]

how do I crack exercise 10?

,, a_n = \sqrt{9n^2 + bn} -3n

[obsidian monolith]

milanesa de pollo [it; its[

[proven void]

find $b \in \mathbb{R}$ s.t. $0 < \lim_{n \to \infty} a_n < 1$

[obsidian monolith]

milanesa de pollo [it; its[

[proven void]

Help

[summer ruin]

find the limit of a_n

[proven void]

another rationalization problem?

[summer ruin]

yes

[proven void]

0 < b < 6

]0; 6[?

that is the only valid interval for b

[desert swallow]

guys

how solve

how u solve this ¬(∃x∃y ¬P(x, y) ∧ ∀x∀y Q(x, y))

demergans law

[viscid thistle]

#proofs-and-logic I guess

[desert swallow]

when i use the vector projection does it still have i and j components

[spring sapphire]

no

student

[proven void]

How to find p knowing its positive?

After rationalizing I get this $\frac{5n^2}{\sqrt{n^p +7} + \sqrt{n^p + 2}}$

[obsidian monolith]

milanesa de pollo [it; its[

[proven void]

Does it mean p is 4?

[summer ruin]

factoring again

[near sentinel]

Can someone help me out please

Q41

[tired portal]

Do you know differentiation of cot^-1 x and cos^-1 x ??

[near sentinel]

Nope

Do uk

Can u pls tell

[tired portal]

Ohkk wait I'll write it and send, was too lazy to write 😅

[near sentinel]

Lol

Thanks a lot!

Also W username

[tired portal]

They're standard results, just search on google for each trigo identity

[near sentinel]

Ya I'll do that

[tired portal]

😁

[near sentinel]

Do we have to do some simplification before differentiating because it seems terrible to differentiate

[tired portal]

If you simplify f(x) it'll be 3cot^-1x & g(x) 2cos^1x

C ans?

[near sentinel]

Ohkk

[near sentinel]

It's D

[tired portal]

Don't mind my writing 😅

Differentiation was not needed 😅

It was 0/0 form so I directly jumped to L'HOSPITAL

[near sentinel]

How did you do thiss

f(x) wala part

[tired portal]

Bro standard result 😭 ITF

Ratta marle vo sab results

[near sentinel]

😭

Rattna hi to nahi ata

[golden cairn]

How

I don’t know how to prove that it’s true for pi/4

[river drift]

if you just want to show that it works, it suffices to plug in pi/4 and show that both sides are equal (since pi/4 is a known angle on the unit circle)

[golden cairn]

I did

[willow bear]

do you know how to prove it's true for x = 30°?

it's the exact same process just the numbers are different

[golden cairn]

Yeah

I know but I don’t know how to do stuff like 1-1/squareroot2

I don’t know how to subtract fractions with square roots

[willow bear]

i mean

[golden cairn]

Without a calculator

[willow bear]

you would encounter roots with 30° as well

[golden cairn]

No

[willow bear]

yes?

[golden cairn]

Well

[willow bear]

cos(30°) = sqrt(3)/2.

so yes you would.

[golden cairn]

But the root isn’t in the denominator

And it cancels out

So it’s easier

For that one

[willow bear]

the root would still happen in a denominator

but ok whatever.

so you know cos(pi/4) = sin(pi/4) = sqrt(2)/2 [= 1/sqrt(2)] yes?

[golden cairn]

How did you write that so quick

I don’t even know what you just wrote

[willow bear]

$\cos(\pi/4) = \sin(\pi/4) = \frac{\sqrt{2}}{2} = \frac{1}{\sqrt{2}}$

[golden cairn]

The symbols like brackets and stuff

[obsidian monolith]

|Ann⟩

[willow bear]

that better?

[golden cairn]

Yes

Yes I do understand that

[willow bear]

i can type 90 wpm in english ¯_(ツ)_/¯

right ok

so then

LHS is $\frac{\frac{1}{\sqrt{2}}}{1 - \frac{1}{\sqrt{2}}}$

[obsidian monolith]

|Ann⟩

[golden cairn]

Yes

[willow bear]

my first idea at seeing this big nasty nested fraction is to clear the inner denominators

here specifically this means multiplying the outer num and denom by sqrt(2)

you'll still have a fraction after this but it will not be nested

[golden cairn]

Ok

[willow bear]

and also let me try to jog your memory by mentioning the technique of rationalizing the denominator

does that sound familiar to you?

[golden cairn]

Yes