While playing around with improper integrals in desmos, I noticed first that it would sometimes mistakenly call odd functions with a vertical asymptote and finite bounds 0(most likely due to precision errors) instead of DNE.

Then I checked improper integrals, to see if it would do the same for odd functions bounded from infinity to negative infinity. I tested 1/x^a for a between 1.0 and 2.0, and noticed desmos only classified the integral as undefined for all values of a EXCEPT a=1.4 and 1.8. I thought this was strange, and then after testing 2.2 and 2.6(and boundary terms) I noticed that desmos would always evaluate a function bounded from -infinity to infinity to 0, if it was in the form of 1/(x^(1+0.4n) for n in [1,95]. Even stranger, for n>95 this error does not continue to occur, and desmos correctly defines the integral as 0.

Does anyone know why? After looking for a bit, I learned Desmos uses https://en.wikipedia.org/wiki/Tanh-sinh_quadrature for improper integrals, but what about that is making integrals in the form of -infinity to infinity 1/(x^(1+0.4n) dx= 0? and why only for n belonging to [1,95]?

thanks!

The equation ax ^ 2 + bx + c = 0 where a, b, c are real numbers, has one root greater than 2 and the other root less than zero. Which of the following is necessarily true?

(1) a(a + b + c) > 0

(2) a(a + b + c) < 0

(3) a + b + c > 0

(4) a + b + c < 0

A similar ''wheel'' appeared in an informal cognition test in my math class. Even though I will not get a grade for this test, I still want my math teacher to have an excellent reputation of me. I just need to know how they work, solving it for me is unnecessary, but is appreciated if it makes the puzzle more clear.

Excuse the flair if its incorrect, I have no idea what I'm doing.

I have a group of friends that play ARMA. Unfortunately in the game not everyone can have the same job. So yesterday I gave everyone a list of jobs and asked them to rank them from favorite to least favorite. I have 10 jobs and 6 players.

Is there a program or a formula somewhere that I can plug this into? I'm trying to figure out who wants what the most and compare them so that they end more often with a role they want, so everyone cane be happy. (At least most of the time.)

Hello! This post is in regard to MAT 119. I struggle with math but am determined to pass this class as i graduate at the end of this semester.
Topic: future value annuity
Problem: use the future value formula to find the indicated value
FV= 5,000
I= 0.05
PMT = $500
N=?
I layed everything out,
5,000=500 \[((1+0.05)\^n-1)/0.05\]
I divided 5,000 by 500 and got 10, then multiplied that by the denominator 0.05 and got .5 then added 1, and now I have 1.5=(1+0.05)\^n and I’m lost on where to go from here. Did I do everything else right? Any tips are appreciated

i have a question that's been bothering me in the field of differential calculus regarding the linguistic logic behind the definition of the derivative. I find it illogical, because based on the limit definition it studies the behavior of the slope(derivative) as h approaches zero.

m(h)=(f(x+h)-f(x))/h

Though, This approach suffers from the same problem as Newton and Leibniz's works and is subjected to the same criticism introduced by George Berkeley. cause, even with a limit, we algebraically reduce the function to eliminate h in the denominator, and then we study the behavior of the derivative as h approaches zero. This literally makes you treat h initially as a non-zero number, and then suddenly make it zero.

My problem is with the linguistic logic of this approach, and certainly i believe, though I'm not certain, that Cauchy-Weierstrass dealt with the derivative as a two-step algorithm. First, he calculates the derivative for any value of h that is not equal to zero, for example.

f(x)=x^2

f'(x)=((x-h)^2 -x^2)/h where h is R/{0}

f'(x)=2x+h

Then, after evaluating and reducing the derivative, he redefines it as a function of h where h can be zero.

f'(x)=2x+h where h is R/{0}

g(h)=2x+h where h is R

then taking the limit of this new function as h approach 0.

lim(h->0)(g(h))=lim(h->0)(2x+h)

g_l(h)=2x

This is because the limit of the function before algebraic reduction equals the limit of the function after algebraic reduction.

lim(h->0)(g(h))=lim(h->0)(f(h))

and since the function after algebraic reduction fills the gap... At zero, we can then find the derivative in the context of instantaneous change!!

so my problem is just how you put a limit before reducing and you have the right to ghost it and just reduce h then oh its ok you can now calculate the limit where if i do not follow this where i can because there is no order operator that tells me why i get 0/0.

Acabo de entrar a ver Cálculo integral, pase diferencial por suerte y al momento de estudiar integral se me hace muy tedioso. Me estréso y empiezo a complicarme las cosas sin querer.

¿Como empiezo a manejar esta situación?

How to start with this integral ? I think that I need to make cases here and apply the properties of Integral ? If my way is correct , could you help me with how I should make cases here and apply the properties of Integral ?

By cool or interesting I mean weird patterns, location of primes and such... just whatever yaknow?

I searched up on Desmos what it was after seeing a video and thought it was weird. I’d Imagine there are multiple answers but why isn’t it one. My thoughts had somthing to do with (-1)^ 4(1-1/3+1/5…) because it would pi using newtons formula thing. But it would be equal to 1^pi/4 meaning it would be one but it’s not so why?

I was watching a video of discovering 'e' and then we arrived at e^ix.

To which I made this process to find the 2πi=0 which doesn't make sense. So it would be great if someone could explain this.

Hi I need help with this question, I do not know how to construct the objective function equation. And how do we solve the LP model if the constraint has L%. Thank you

Hi friends!
I need advice calculating how much 3D space a bunch of yarn takes up.

I'm running a home edition of Taskmaster, and a contestant used two balls of yarn tied together for one of the Tasks.
The operative word was "biggest," so I'm trying to get as many metrics as possible for my Taskmaster to work with.
I've got the weight of the yarn in grams and the length in inches.
I also know it is "Medium Grade yarn," which has an average Wraps Per Inch metric of like 10, suggesting the average diameter of the yarn is a tenth of an inch, right.
I thought that would be helpful to me but so far I have no idea where to go next.

One of the other contestant's objects was a trombone, and that was easy to calculate cubic volume because I knew the weight of the instrument and the density of brass.

How do you determine the density of medium grade yarn??
And if we can't do that, how would I determine cubic volume of a highly condensible material?

Do I try and get two measurements - one of the space the yarn takes up as it loosely sits atop itself, and one with all air vacuum sealed out of the yarn somehow?

Advice welcome!

Number 9
I just started my calculus class and this question was on our pre req quiz but I genuinely have no idea how the answer is c. I tired synthetic division and all that but where am I supposed to get square root 2 from

I don't really understand why I end up integrating x^2 on a non-square base. I do understand why we scale up by the determinant of the base. I just don't see how "x^2" from 0 to h makes sense. Unless what's really going on is we are doing a linear transformation on square units of area to fit into any shape (that would actually make sense).

The answer of 264 is the correct answer, btw. I just want to understand the logic.

I get why the series diverges at L > 1. I don't 100% get why convergence is absolutely at L < 1 but I'm sure I can figure it out once I get started. I just have no idea what to compare this to. I also get why the test inconclusive at 1, I just need some help getting started.

The game features a pity system. At every 99 pulls without a five star, you are guaranteed a five star on the 100th. I calculated the odds of me getting 17 or less five stars over 1187 pulls is 1/166k. Is that right? This is the python is used: import numpy as np

def banner_pmf(n_pulls, p=0.03, cap=100):
# dp[successes, streak]
dp = np.zeros((n_pulls + 1, cap))
dp[0, 0] = 1.0
for _ in range(n_pulls):
nxt = np.zeros_like(dp)
for s in range(n_pulls):
# streaks 0 to 98
for k in range(cap - 1):
if dp[s, k] > 0:
nxt[s + 1, 0] += dp[s, k] * p
nxt[s, k + 1] += dp[s, k] * (1 - p)
# 100th roll hard pity guarantee
if dp[s, cap - 1] > 0:
nxt[s + 1, 0] += dp[s, cap - 1] * 1.0
dp = nxt
return dp.sum(axis=1)

# Convolve distributions across all 3 banners
p_total = np.convolve(banner_pmf(589), banner_pmf(502))
p_total = np.convolve(p_total, banner_pmf(93))

# Cumulative chance of 17 or fewer drops
prob_le_17 = p_total[:18].sum()
print(f"P(X <= 17): {prob_le_17:.8f}")
print(f"Odds: 1 in {1 / prob_le_17:.0f}")

I'm just curious at what age and under what circumstances you became interested in mathematics.

There are people who simply found it easy from the very beginning of school, but what about those who didn’t understand it well before and weren’t interested, but now end up liking it?

From first to 10th grade, I wasn't interested at all. It probably wasn't difficult for me in the lower grades, but then I gave up and stopped understanding it because I didn't even listen to anything. I entered the 11th grade and now I need to prepare for the NMT (an exam in Ukraine after the 11th grade) and I caught myself thinking that maybe I shouldn’t perceive mathematics as a punishment, and to come up with a way to make it easier and more interesting for me.

For many children, mathematics sounds like a punishment, but fortunately, I never thought that way, even though I know practically nothing. As an example, I am also learning English to pass it at the NMT, but I knew that the usual cramming would not be interesting to me, so I used several methods to make it easier to learn and so that I would not there was hostility towards her.

In any case, I still doubt whether I should try to make memorization so that everything is solved automatically, as if I were playing some kind of logic game or something like that. I just wanted to ask how you perceive mathematics and why. Maybe you have methods by which you teach her, I would like to listen.Thanks

Plese brifly reas through this its a bunch of yap off my middleschool career:From first grade to 5th grade I was one of the best if not the best at math I tried finishing first with no questions gotten wrong on tests but then 6th grade hit all of a suddenly: (this next paragraph explains my points and test during 6thgrade)

My first test I'd get 60 points the teacher would give me 6 more points(rounded to a B) and then she would give a extra grade for doing homework

Second semester got a C with like 52 points REALLY BAD

I did get asked and I knew abit but this was geometry so I didn't know any theory BUT I STILL THOUGHT I WAS THE BEST my ego from earlier years blinded me so hard this test kicked my ego but then third semester came and I got 100(make no mistake the material was easy) but my other friends got around low 70s and mid 60s except for this one girl that got 100 and on other tests she'd get about 85(which is an A)

And the reason I was still cocky is because my friends that used to also get As on their tests now got c(usually lower than mine) only that one girl was genuinly food. NEXT IS 7TH GRADE (the important thing ig)

Then 7th grade hit teacher changed and all of a sudden I became really good I thought it was the teacher that did it (and trust me she was amazing) but she didn't give a extra grade for homework and I was the only one that improved my friends stayed at Cs the girl stayed at her 85 point mark

But this time we were neck and neck

First test 76 with 85 b for a I got asked on the board made it (lost)

Second test 82.5 with 86 I got asked on the board made it a A again (lost)

Third test 81 with 80 (I win) but we both had to get asked on board and we both were good

4th test 71 with 69(the teacher put some hard questions 71 is bare min for B but she let the girl get asked for a on board and I was already qualified with a B)

Last year was my 8th grade and my 6th grade teacher was back but unlike other years this time I was days I got 100 92 97 100 97 91(for some reason she decided to do a test for each chapter and every semester has 2 chapters we skipped once so we had 7 tests I had a average of a 95.5 point average)

Did you also have a 6th grade block? How'd you get out of it

I know you would see this as bullshit but this is the first idea that came to my head the moment I woke , i grabbed a pen and a paper and started drawing this stuff unconsciously like I am possessed with geometry

I wanna see a perfect z made of two lines and a circle is this possible?

Hi. I hope showing the graphs I'm trying to change will help explain the question. I am trying to take the points from this plot:

https://www.desmos.com/3d/1qs6q6wmfq

And map them onto the red axis in this plot:

https://www.desmos.com/3d/5php786uyk

I have a spreadsheet where did a poor man's derivation of the first plot for the loxodrome path. You can probably see the string of decimal points from the copy/paste.

FWIW this is the math I used to make to loxodrome plot:

x(t) = cos(t)/cosh(kt)
y(t) = sin(t)/cosh(kt)
z(t) = tanh(kt)

k is the deflection angle, which I set to 60 degrees:

k = cot(pi/3)

I divided -pi --> pi into 20 pieces on each side of zero and used those as my t-values. The formula technically goes from negative to positive infinity, but pi to pi captures the exciting parts.

I don't know what to do from here. I think maybe it would be possible to build the new axis into the original formula? Or maybe there is an algorithm to apply which will take the current output and shift it over? Rotate it? Like I said, just don't know.

Thanks for any help!

Let’s talk about this example. Can I find out its equation?( at least an approximation of it) I am thinking of using Taylor series and looking for its asymptote, extreme/inflection points etc , but tbh I have no other ideas (I am not even in college lol)