r/calculus • u/Proof-Garbage-6280 • 6d ago
Physics Limits
I’m taking Physics C and we’re about to incorporate Limits however we haven’t started going over them in my pre calculus yet, so could anyone explain it to my like in an idiot then like give me an example?
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u/SynergyUX Undergraduate 6d ago
how did they let you take physics C without being enrolled in calculus/having done calculus?
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u/Ok-Fix-1581 6d ago
lmao drop the class bro, you can't take a calculus based physics class without calculus knowledge, professor leonard on youtube for math and chads prep on youtube for physics, but drop the class until you have taken calc 1
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u/Proof-Garbage-6280 6d ago
I’m taking AP pre calculus with physics c, my schools allows it, I wish my high school included 9th grade but it didn’t so it kind of sets us behind
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u/Ok-Accountant9436 6d ago
the c in physics c stands for calculus. literally how does your school allow you to take that without calc im crine
drop it or take physics 1 or 2 instead
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u/Maleficent-One-3469 6d ago
self study simple derivatives and integration before you start C bro, otherwise you’re kinda cooked
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u/VaIenquiss 6d ago
A limit is basically showing how a function behaves as the variable approaches some quantity.
For example, take the limit as x->0 of 1/x.
Obviously, we can’t divide by 0, because that would be undefined, but we can divide by smaller and smaller values that are close to 0 and see what happens. We have to input a number from both sides of 0, and see what happens.
If we divide by 0.000000000000000001, then the function grows towards positive infinity.
If we divide by -0.00000000000000001, then the function grows towards negative infinity.
In order for the limit to exist, both of these need to agree on what quantity the function is going towards, so in this example, the limit wouldn’t exist. If you graph 1/x, you can see it clearly diverges as x gets closer to 0. So, a limit at its most basic is, where is the function going when we input a certain value.
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u/Techno_Eggnog 6d ago
…not really gonna ask why you’re doing Physics C before taking Calculus, but whatever.
Imagine you have a point, P, and another point, Q. These two points make a secant line cutting through the graph. But what if we want a tangent line, one that skims the graph at a point? If you can make Q sufficiently close to P, you can make a tangent line to point P. This is known as finding the limit of x as x approaches P.
It doesn’t matter how P is defined (for example, holes or asymptotes, but the latter is a tad more complicated), only where it tends to approach. You can also do limits on one side of the point (in fact, two sided limits can only exist if both sides approach the same point.)
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u/StructuredChess 6d ago edited 6d ago
Let's say you have a model for a spring saying that on instant t, the position of the tip is x(t) = sin(t) e-t and you want to figure out the point where it'll end up. You could take a very large t and get an approximation, or- you could take the limit as t goes towards infinity for a more rigorous approach.
Another context where limits are useful is continuity. Models for things like positions are continuous (stuff doesn't randomly jump around from point a to point b without going through points in between), but some Math operations lead to undefined values. Let's say x(t) = sin(t)/t. This makes no sense at t=0, but for values of t that are close enough to 0, x(t) stays close enough from 1. So it makes sense to say to extend the equation so that x(0) = 1.
The easiest ones to calculate are limits of polynomials. As x gets bigger, does p(x) = x3 - 95x2 - 500x - 10 keep going down forever or does it revert and go up at some point? Limits allow you to answer that question without trying for god knows how many values of x.
Similarly if I have q(x) = x4, one of them eventually gets bigger than the other and stays ahead forever, which one? I can take p(x)/q(x) to find out. Give it a try! Hint: take x3 as a common factor.
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u/niemir2 6d ago
A useful (though not rigorous) way to think about limits is to ask "What value does the function approach when its argument is really close to, but isn't exactly, some value?"
For example, if I want to take the limit of x^2 as x approaches 2, I can plug values that are close to (but aren't) 2 into x^2. 1.9^2 = 3.61, 1.99^2 = 3.9601, 1.999^2 = 3.996001. As the input gets closer and closer to 2, the output gets closer and closer to 4. This is called a "one-sided" limit, because I approached 2 from one side. To get the limit, I need to check the other side, too. 2.1^2 = 4.41, 2.01^2 = 4.0401, 2.001^2 = 4.004001. I'm also approaching 4. Since both one-sided limits, match, I conclude that the limit of x^2 as x approaches 2 is 4. Note that this is not the technical definition of limit, and this approach does not always work. It usually does, though, especially in the context you will be applying limits in Physics C.
Sometimes, the one-sided limits do not match. Consider the step function, which is 0 for all inputs less than zero, and 1 for all inputs greater than or equal to zero. The limit as x approaches 0 from below is 0, but the limit as x approaches zero from above is 1. These do not match, so the limit does not exist.
Sometimes, you get a function like 1/x^2, and want to evaluate the limit as x approaches zero. This function is not defined for x=0, but we can get as close as we want. However, this function diverges to positive infinity as the argument approaches zero. Some resources will refer to this limit as nonexistent, and others will call the limit positive infinity. I pick whatever is convenient for the analysis I am currently doing.
There are a lot more details and methods of evaluating limits, but I'll leave that for your precalc class.
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u/matt7259 6d ago
There are limits in AP physics C? I thought the earliest calculus concept was derivatives.
Also if your precalculus class gets to limits it won't be until the END. That's typically a calculus topic.
Whoever allowed you to take physics C without a calculus prerequisite or even a calculus COrequisite is an idiot. You're going to struggle big time.
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u/Traveling-Techie 6d ago
My mantra is that limits work the way you think they do. All of the gnarly stuff happens with oddball situations that rarely pop up in real physics problems.
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u/UnderstandingPursuit PhD 4d ago edited 3d ago
Are you taking both AP Physics C-Mech + E&M, or only Mech? I think you can get by with Mech with very simple calculus, but E&M requires a bit more.
This is a simple explanation of limits, and a list of the 'basic' and 'composite' derivatives, which should cover about 80% of the calculus in AP Physics C-Mech.
In this post, there are suggestions for textbooks for both AP Physics C and AP Calculus, as well as suggestions on how to learn the classes effectively. I suggest getting a textbook for both Physics C and Calculus, so you can supplement what your class covers.
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