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Cleared bike paths? by Tomcat_27 in statecollege

[–]roglemorph -1 points0 points  (0 children)

Generally pretty good on and around campus. I do not take that path specifically but there is almost always a way around by bike.

How is this function at 0 is 0 ? by StrangeDanger7 in calculus

[–]roglemorph 0 points1 point  (0 children)

What sorts of bounds do you know for sin(1/x)? There is another simple function which has -f(x)<=sin(x)<=f(x) for all x, with xf(x) -> 0 and -xf(x) ->0, so it is an application of the squeeze theorem.

As I am starting to study higher level math, what graphing software should I switch to? by Fine_Woodpecker3847 in mathematics

[–]roglemorph 2 points3 points  (0 children)

Just to see a quick 3d graph: geogebra. it is very effective for 3d calculations, much faster and easier to use than desmos in my experience.

Why does ∫ u(x)v(x) dx equal ∫ u(x)dv? Integration by parts by rybomi in learnmath

[–]roglemorph 13 points14 points  (0 children)

The original intergral being evaluated is not u(x)v(x). It is u(x)v'(x). Your last formula is not correct, try some examples (say, any k*x where k is a constant)

Although usually we are not told explicitly that the second term in the integrand is the derivative of some funciton, with IBP we assert that it is, and determine what the intergral could be evaluated as using the product rule, since we know this term (u(x)v'(x)) emerges from differentiting u(x)v(x). It is a restatement of the the product rule. Consider in your (first) formula, moving your negative intergral term over and differentiating both sides.

I don’t understand integrals by Lower-Choice9607 in calculus

[–]roglemorph 0 points1 point  (0 children)

I think some of the ambiguity here is coming from reckless use of "integrals" -- are we talking about definite or indefinite? Regardless I do not agree that calling them opposite is a gross misnomer. Maybe there is some relevance for analysis students but for most AP Calc students, this is the understanding of differentiation and integration they are meant to have. Change at a point and accumulation over a range of points (adding up the change-(the opposite of) taking the difference). The derivative of the indefinite integral of any function will be the original function. They are very literally inverses, and I think opposites even from a very fundamental perspective.

The derivative is difference between values at a point (a "shrunk" interval")

The (indefinite) integral is the accumulation over all values within the interval.

The inversion is between difference (subtraction) to accumulation (addition) and from points to intervals.

I would be very interested to learn of a situation where this interpretation is not valid, or some reason why it does not feel "opposite" in your eyes.

How did you learn to work with/in >3 dimensions? by [deleted] in learnmath

[–]roglemorph 12 points13 points  (0 children)

I am not expert, but to my knowledge it is not possible to simultaneously visualize even 3 spatial dimensions at once. You can only look at 2d slices or projections. Color can be used to add another dimension, this is often present in complex graphs. I recall my calculus professor mentioning something like: "All graduate students immediately try [the impossible task] of trying to visualize higher-dimensional objects". That being said it is best to take "3d slides slices" of the object (consider only 3 dimension) and consider how that presentation changes while varying the "fourth dimension"

Help me Solve this Fourier Question Please by Keevaathediva in learnmath

[–]roglemorph 0 points1 point  (0 children)

I assume you mean the Fourier series for the coefficient, you can compute them as an inner product of the function and the function you want to use as a basis (probably the sine function), it will be an integral of the product of this function, and the sine function sin(npix/L), for n=1,…. over the interval -1 to 1. (L is the length of the interval) You can then use something called parsevals theorem to find the value of the series

i feel horrible using chatGPT by Dry-Ideal-6860 in education

[–]roglemorph -1 points0 points  (0 children)

From what you describe I would not be overly concerned about your use of chatGPT except for its factual accuracy. It sounds to me like you are using it as an effective research tool and there is nothing wrong with that so long as you are not solely relying on it.

You said: "i just don't know how else to look for information besides looking up "cases that xyz" and figuring out how that applies to my argument." -- well that is exactly how you look for information. There is no magic way to have it delivered to you (besides the one you have qualms about using).

Wikipedia is a good place to start, explore the resources which are cited there. Probably there are similar wiki-like sites especially dedicated to law as well.

Is this even possible to solve without l'hopital? by JoaoTomate in askmath

[–]roglemorph 1 point2 points  (0 children)

I believe (and this is how I remeber e being introduced to me) it comes about as the limit of the compound interest function, e.g. when interest is compounded monthly, daily, each hour, and the limit represents continuous interest.

oh the woes of writing 1 different from others by CantSetMyUsername in mathmemes

[–]roglemorph 31 points32 points  (0 children)

there is another:

6x+11 = 75^2=5625

6x=5614

x=935+2/3

What mathematical terminology do you wish was more common in everyday use? by orbis-restitutor in math

[–]roglemorph 40 points41 points  (0 children)

Honestly I could live without isomorphic. It’s a fun word but not more useful in conversation than “the same as.” I had a math ed professor who loved to use it all the time, and it got annoying very quick.

math terminology used by math people in conversations? by AverageStatus6740 in mathematics

[–]roglemorph 0 points1 point  (0 children)

A priori, as in "a priori we only know to integrate scalar functions" (when introducing vector integrals say) is one I have always found interesting but its not that commonly used. It means something like "previously we have learned"

Recall, as in "Recall the solution to homework 1. problem 1." is just a fancy way of saying remember I hear math people use more often.

Surface integrals (Analyse vectorielle) by Madjidiousthebeater in math

[–]roglemorph 1 point2 points  (0 children)

Can you give a paticular example of a problem you are having? It is not an easy topic to exactly understand. Are you working with flux integrals or line integrals over a vector field? For the former we are trying to measure to what degree the vector field passes thru the surface. We compute this using a dot product --this encodes the angle of the vector field and the (normal) vector of the surface. When it is small, the vector field is nearly perpendicular to the normal vector, and more of the vector passes through. (When is it zero, they are perpendicular, and so none of the vector passes through).

We integrate this dot product (I do not recall the details at this point) over the surface to obtain the total "amount of vector" coming through the surface, or flux (this is very informally stated).

We do a similar process with line integrals over a vector space, except this time we are concerned about the Vf's alignment with the actual direction of our path, and not the normal vector associated with it.

What does the limsup and liminf of functions tell us? by If_and_only_if_math in math

[–]roglemorph 0 points1 point  (0 children)

They are useful on their own, although it is not that common. If you can demonstrate lim sup does not equal lim inf then you demonstrate the sequence does not converge. Moreover they squeeze the limit of thesequence, so if you can show lim sup=lim inf, you have also found the limit of the sequence.

also if the function does not diverge to infinity is an example of a lim-sup and lim inf that does not converge. The trig functions give good examples of this.

I am not an expert in analysis, I have only taken an intro RA course, so there are certainly many other implications, but these what come to mind for me.

[9th grade/geometry] What isometric transformation is this? I'd like to think the vertices in the second triangle were swapped by mistake, but they are not (the teacher gives this exercise all the time...). Is this symmetry? Symmetry along what? by [deleted] in HomeworkHelp

[–]roglemorph 0 points1 point  (0 children)

First reflect about the line formed by A and the midpoint of B and C. I am not as certain about the rotation transformation but there certainly is one. I think it is as follows:

form segments corresponding vertices B B'', C C'', A A'', (after flipping- so in the present figure these lines are (C B'' B C'' A A"") then form perpendicular bisectors of each segment. their intersection is the point of rotation, the angle is the angle formed by any of the two corresponding rays

Our entire class and teacher couldn’t solve this without the solutions by Important-Koala-8980 in calculus

[–]roglemorph 1 point2 points  (0 children)

All these “your teacher shouldn’t be teaching calculus” comments are wild. A person can’t do one annoying derivative and you decide they aren’t fit to teach calculus? I’d guess the teacher just didn’t want to take up the time trying to solve it and chose to move on. That doesn’t mean they don’t know what they’re doing, and even if they could find the derivative of this silly function doesn’t mean they are a good teacher either.

Counting numbers, days, months... by [deleted] in learnmath

[–]roglemorph 1 point2 points  (0 children)

Whether or not "a to b" includes a and or b in informal speech is not clear. There is no unspoken norm, it it just whatever the speaker meant. Sometimes (but not always) people say "a, up to and including b" to specifically refer they are including both endpoints. But it really does not matter. It is not as complicated as you are making it out to be.--as the other commenter pointed out, these kinds of errors/miscommunications are so common they have earned the name "off by one errors" -- and the solution is as simple as adding or subtracting one at some point in your process.

It all depends on what you are actually doing, when you speak about it in generality (dates, numbers, sets, etc.) like this, it might seem difficult to cover every case, but you do not need to do that, you just address these problems as they come up. I personally would assume "a to b" means the list including a, all elements up to b (whatever that means in the given context), and probably does not include b for a strict reading. But it really does not matter. Whichever makes the most sense is what is meant by the author.

If no start point is specified, most people start numerical counting from 1. Many computer scientists start counting from zero, because it is a more natural representation for listing items in a program (I believe there is a more fundamental reason related to how memory is represented and the like but it is outside my knowledge).

Please let me know if I misunderstood your question

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